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

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2020 Workiva-->
<!--r:437e8585-2039-4da2-bcfe-ff4c7532c724,g:6b9a2dbe-f5b9-4699-b916-c39143ea3b99-->
<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-20200729.xsd#DocumentandEntityInformationDocument"/>
  <link:calculationLink xlink:role="http://www.livanova.cyberonics.com/role/DocumentandEntityInformationDocument" xlink:type="extended"/>
</link:linkbase>