A man in a black rubber suit has been jumping out and making indecent gestures at people around Claverham and Yatton.
In his most recent appearance, the man approached a woman in the Claverham Park area just before midnight on Thursday.
He made an inappropriate gesture but ran away after the woman stood her ground.
Police say no one has been physically hurt during any of his appearances, and officers have increased patrols in the area as a result of the distress the man in the 'gimp suit' has caused.
They insist they are doing all they can to work with the community to identify the unknown man.