Lieutenant Commander John Alan Jones, 58, was found guilty of seven counts of indecency without consent.
The military court heard that two of the incidents, which occurred last year while Jones was serving on a supply ship, involved the young female sailor lying across his lap and him smacking her bare buttocks.
Jones told her it was a “test to see how disciplined and compliant you were going to be”, in a recording she secretly made during one of their encounters which was played to the court.
Jones admitted some of the behaviour but denied it was non-consensual or amounted to an indecent act.
He was expected to be sentenced on Wednesday and faces a maximum of five years in prison for each indecency offence.
Sentencing submissions were heard on Tuesday and a defence ministry spokeswoman told AFP: “A punishment has not yet been awarded and it would be inappropriate to comment further during the sentencing process.
“Navy is working to ensure that the sailor who came forward is being offered all the care and support she may need.”
Australia’s military has gained a reputation for a drinking, sexist culture, and the defence force’s treatment of women is currently under government review.
A recent report into the nation’s premier military academy in Canberra found sexual harassment was widespread, following a scandal over a young female cadet unwittingly filmed and broadcast having sex with a colleague.