<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2021 Workiva-->
<!--r:a3a6ba83-bf73-47d1-a3cc-7e2c1e1cceeb,g:c9d596c9-278a-4676-a8cd-045aa7cd3aca-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.anaptysbio.com/role/CoverPage" xlink:type="simple" xlink:href="anab-20210504.xsd#CoverPage"/>
  <link:calculationLink xlink:role="http://www.anaptysbio.com/role/CoverPage" xlink:type="extended"/>
</link:linkbase>