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

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2021 Workiva-->
<!--r:0bc0128f-a898-4938-9058-0edc0c662069,g:e41c2eef-fd8c-4636-a6b5-c62ea8e5ec6e-->
<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.livanova.cyberonics.com/role/DocumentandEntityInformationDocument" xlink:type="simple" xlink:href="livn-20210409.xsd#DocumentandEntityInformationDocument"/>
  <link:calculationLink xlink:role="http://www.livanova.cyberonics.com/role/DocumentandEntityInformationDocument" xlink:type="extended"/>
</link:linkbase>