Jonathan Ansell, 26, last made contact with relatives in Scotland two weeks ago and has not been heard from since.
He told his mother he was in Melbourne but did not have a place to stay or any money and had lost his passport.
Mr Ansell, thought to be from Glasgow, has been in Australia for around two years.
His family describe him as a quietly-spoken man and said they believe he may not approach anyone for help if he was in trouble.
He is described as being of Caucasian appearance, 5ft 9in with a fair complexion and short, light-brown/dark blonde hair. He has a Scottish accent.
Police said he may have travelled within the Victoria area or interstate in Australia.
A Foreign Office spokesman said: "We are aware of reports of a missing British national in the Melbourne area. We are liaising with the local police and providing consular assistance to his family."