SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. 4)*

KALVISTA PHARMACEUTICALS, INC.

(Name of Issuer)

Common Stock, par value $0.001 per share

(Title of Class of Securities)

483497103

(CUSIP Number)

Brent Faduski

SVLSF IV, LLC

One Boston Place

201 Washington Street, Suite 3900

Boston, MA 02108

(617) 367-8100

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

April 2, 2019

(Date of Event Which Requires Filing of This Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box   ☐.

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See § 240.13d-7 for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

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CUSIP NO. 483497103

This Amendment No. 4 to Schedule 13D (“Amendment No. 4”) amends the Schedule 13D originally filed with the Securities and Exchange Commission (the “Commission”) on February 7, 2017 and amended by Amendment No. 1 filed with the Commission on March 2, 2017, Amendment No. 2 filed with the Commission on February 26, 2019 and Amendment No. 3 filed with the Commission on March 20, 2019 (together, the “Prior Filing”), to disclose certain transactions in the Common Stock, par value $0.001 per share (the “Common Stock”), of KalVista Pharmaceuticals, Inc. (the “Issuer”), including the disposition of some of the shares of the Issuer’s Common Stock held by Reporting Persons. Except as specifically amended by this Amendment No. 4, each Item of the Prior Filing remains unchanged. All capitalized terms contained herein but not otherwise defined shall have the meanings ascribed to such terms in the Prior Filing.

This statement relates to the Common Stock, par value $0.001 per share (the “Common Stock”), of KalVista Pharmaceuticals, Inc. (the “Issuer”). The address of the principal executive offices of the Issuer is 55 Cambridge Parkway, Suite 901E, Cambridge, Massachusetts 02142.

Item 2 of the Prior Filing is hereby amended and restated in its entirety as set forth below:

(a) This statement is filed by: (i) SV Life Sciences Fund IV, L.P. a Delaware limited partnership (“SVLS IV LP”) and SV Life Sciences Fund IV Strategic Partners, L.P. a Delaware limited partnership (“Strategic Partners” and together with SVLS IV LP, the “Funds”), each direct owners of the shares of Common Stock of the Issuer (together, the “Shares”); (ii) SV Life Sciences Fund IV (GP), L.P., a Delaware limited partnership (“SVLS IV GP”) and general partner of SVLS IV LP and Strategic Partners; and (iii) SVLSF IV, LLC, a Delaware limited liability company and general partner of SVLS IV GP. Each of SVLS IV LP, Strategic Partners, SVLS IV GP and SVLSF IV, LLC are sometimes individually referred to herein as a “Reporting Person” and collectively as the “Reporting Persons.”

(b) The principal business address of the Reporting Persons is c/o SV Health Investors, One Boston Place, 201 Washington Street, Suite 3900, Boston, MA 02108. The principal business address of any person or entity listed on Schedule A annexed hereto is set forth on Schedule A annexed hereto.

(c) The principal business of the Reporting Persons is international life sciences venture capital investments. SVLS IV LP and Strategic Partners are private venture capital funds. SVLS IV GP is the general partner of SVLS IV LP and Strategic Partners. SVLSF IV, LLC is the general partner of SVLS IV GP. The principal business of the persons or entities listed on Schedule A annexed hereto is listed on Schedule A annexed hereto.

(d) No Reporting Person nor any person or entity listed on Schedule A annexed hereto has, during the last five years, been convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors).

(e) No Reporting Person nor any person or entity listed on Schedule A annexed hereto has, during the last five years, been party to a civil proceeding of a judicial or administrative body of competent jurisdiction and as a result of such proceeding was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, federal or state securities laws or finding any violation with respect to such laws.

(f) Each of the individuals listed on Schedule A annexed hereto are citizens of the country set forth on Schedule A annexed hereto. Each of the Reporting Persons are organized under the laws of the State of Delaware.

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CUSIP NO. 483497103

Item 5 of the Prior Filing is hereby amended and restated in its entirety as set forth below:

(a) The aggregate percentage of Shares reported owned by each person named herein is based upon 17,247,348 shares of Common Stock outstanding as of March 10, 2019 as indicated in the Issuer’s Quarterly Report on Form 10-Q filed March 14, 2019.

The Funds, SVLS IV GP and SVLSF IV, LLC may each be deemed to beneficially own, in the aggregate, 1,769,576 shares of Common Stock, constituting approximately 10.26% of the Common Stock outstanding.

As of the close of business on the date of this filing, SVLS IV LP owned directly 1,720,725 shares of Common Stock, constituting approximately 9.98% of the Common Stock outstanding.

As of the close of business on the date of this filing, Strategic Partners owned directly 48,851 shares of Common Stock, constituting approximately 0.28% of the Common Stock outstanding.

SVLS IV LP and Strategic Partners (each a “Fund”, or collectively the “Funds”) may be deemed to beneficially own the shares held by each other Fund because of certain contractual relationships among the Funds and their affiliates. The Funds disclaim beneficial ownership of shares held by any other Fund except to the extent of any pecuniary interest therein.

SVLS IV GP, the general partner of SVLS IV LP and Strategic Partners, may be deemed to beneficially own the shares held by SVLS IV LP and Strategic Partners. SVLS IV GP disclaims beneficial ownership of shares held by SVLS IV LP and Strategic Partners except to the extent of any pecuniary interest therein.

SVLSF IV, LLC, the general partner of SVLS IV GP, may be deemed to beneficially own the shares held by SVLS IV LP and Strategic Partners. SVLSF IV, LLC disclaims beneficial ownership of shares held by SVLS IV LP and Strategic Partners except to the extent of any pecuniary interest therein.

The investment committee of SVLSF IV, LLC, comprised of the members as set forth on Schedule A, may be deemed to beneficially own the shares held by the Funds as it controls voting and investment decisions over the Issuer’s shares held by the Funds by a majority vote. Each member of the investment committee disclaims beneficial ownership over shares held by the Funds except to the extent of any pecuniary interest therein.

(b) Each of SVLS IV LP and Strategic Partners have sole power to vote and dispose of the Shares they own directly.

Each of Strategic Partners, SVLS IV GP and SVLSF IV, LLC may be deemed to have sole power to vote and dispose of the Shares reported in this Schedule 13D owned directly by SVLS IV LP.

Each of SVLS IV LP, SVLS IV GP and SVLSF IV, LLC may be deemed to have sole power to vote and dispose of the Shares reported in this Schedule 13D owned directly by Strategic Partners.

Voting and investment power over the Shares of Common Stock beneficially owned by the Reporting Persons has been delegated to SVLS IV GP. SVLS IV GP has delegated voting and investment decisions to SVLSF IV, LLC, which in turn has delegated such decisions to an investment committee comprised of the members as set forth on Schedule A. Each Reporting Person and each member of the investment committee disclaims beneficial ownership of the Shares except to the extent of any respective pecuniary interest therein, as described in Item 5(a).

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CUSIP NO. 483497103

(c) Except as follows, none of the Reporting Persons, nor, to the best knowledge of the Reporting Persons, without independent verification, any other persons named in Item 2 hereof, has effected any transaction in the Common Stock during the past 60 days:

On February 19, 2019, SVLS IV LP sold 17,912 shares of the Issuer’s Common Stock and Strategic Partners sold 508 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $20.7328 per share. These shares were sold in multiple transactions at prices ranging from $20.04 to $21.61.

On February 20, 2019, SVLS IV LP sold 22,594 shares of the Issuer’s Common Stock and Strategic Partners sold 641 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $20.0159 per share. These shares were sold in multiple transactions at prices ranging from $20.00 to $20.115.

On February 21, 2019, SVLS IV LP sold 167,779 shares of the Issuer’s Common Stock and Strategic Partners sold 4,764 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a price of $20.60 per share.

On March 4, 2019, SVLS IV LP sold 42,181 shares of the Issuer’s Common Stock and Strategic Partners sold 1,197 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $22.907 per share. These shares were sold in multiple transactions at prices ranging from $22.02 to $23.02.

On March 5, 2019, SVLS IV LP sold 31,439 shares of the Issuer’s Common Stock and Strategic Partners sold 893 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $23.0365 per share. These shares were sold in multiple transactions at prices ranging from $22.52 to $23.34.

On March 18, 2019, SVLS IV LP sold 255,224 shares of the Issuer’s Common Stock and Strategic Partners sold 7,246 shares of the Issuer’s Common Stock, in a same-way open market transaction executed by a broker-dealer at a price of $26.70 per share.

On March 26, 2019, SVLS IV LP sold 29,262 shares of the Issuer’s Common Stock and Strategic Partners sold 831 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $29.6975 per share. These shares were sold in multiple transactions at prices ranging from $28.68 to $30.01.

On March 27, 2019, SVLS IV LP sold 56,318 shares of the Issuer’s Common Stock and Strategic Partners sold 1,599 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $29.0592 per share. These shares were sold in multiple transactions at prices ranging from $28.14 to $30.425.

On March 28, 2019, SVLS IV LP sold 35,653 shares of the Issuer’s Common Stock and Strategic Partners sold 1,012 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $27.801 per share. These shares were sold in multiple transactions at prices ranging from $27.26 to $29.10.

On March 29, 2019, SVLS IV LP sold 34,133 shares of the Issuer’s Common Stock and Strategic Partners sold 969 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $28.396 per share. These shares were sold in multiple transactions at prices ranging from $27.62 to $29.13.

On April 1, 2019, SVLS IV LP sold 51,373 shares of the Issuer’s Common Stock and Strategic Partners sold 1,458 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $27.6582 per share. These shares were sold in multiple transactions at prices ranging from $26.84 to $28.78.

On April 2, 2019, SVLS IV LP sold 8,888 shares of the Issuer’s Common Stock and Strategic Partners sold 253 shares of the Issuer’s Common Stock, in a series of same-way open market transactions executed by a broker-dealer at a weighted average price of $28.7638 per share. These shares were sold in multiple transactions at prices ranging from $27.53 to $29.14.

(d) No person other than the Reporting Persons is known to have the right to receive, or the power to direct the receipt of dividends from, or proceeds from the sale of, the Shares.

(e) Not applicable.

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CUSIP NO. 483497103

SIGNATURES

After reasonable inquiry and to the best of his knowledge and belief, each of the undersigned certifies that the information set forth in this statement is true, complete and correct.

Dated: April 3, 2019

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CUSIP NO. 483497103

SCHEDULE A

Information regarding members of the investment committee of SVLSF IV, LLC

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