UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16

UNDER THE SECURITIES EXCHANGE ACT OF 1934

May 29, 2020

Commission File Number: 001 - 38178

Zealand Pharma A/S

(Exact Name of Registrant as Specified in Its Charter)

Sydmarken 11

2860 Søborg (Copenhagen)
Denmark

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F x            Form 40-F ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1):  ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7):  ¨

Furnished as Exhibit 99.1 to this Report on Form 6-K is a company announcement of Zealand Pharma A/S or the Company, dated May 29, 2020, disclosing information on transactions in Zealand's shares or related securities conducted by persons discharging managerial responsibilities and/or their closely associated persons. Exhibits 99.2, 99.3 and 99.4 provide details on these transactions.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Zealand Pharma A/S
By:	/s/ Matthew Dallas
	Name:	Matthew Dallas
	Title:	Chief Financial Officer

Date: May 29, 2020

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EXHIBIT INDEX

Exhibit No.	Description
99.1	Company announcement dated May 29, 2020
99.2	Exercise of warrants – A. Steensberg
99.3	Sale of shares – A. Steensberg
99.4	Sale of shares – A. Steensberg

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