Maverick LNP backbencher Jason Costigan has been suspended from the party, after a complaint alleging he harassed a woman.

A woman complained to the LNP that Mr Costigan allegedly harassed her 18 year old daughter after she returned to her grandparents home, where he was staying temporarily, and found him shirtless.

Mr Costigan will be suspended until the LNP state executive meets on Friday, February 1, when he could be expelled. If expelled, Mr Costigan would join the crossbench at the first sitting of the Queensland Parliament for 2019 in less than two weeks.