A company non-executive director Andrew Young has stepped in as interim chief executive until a permanent replacement for Paton has been appointed.
Cue said a new chief executive should be in place by next March.
Paton joined the company in February 2011 and had "decided to return to Darwin to pursue other interests", said Cue.
Cue's share price has lost half its value since early June this year, despite the fact it has long established oil production in Indonesia, New Zealand and Papua New Guinea.
