Maribyrnong Crime Investigation Unit detectives are investigating a series of incidents in the vicinity of Cruickshank Park in Yarraville last month.
It is believed an unknown male has followed several females through the park and surrounding streets between the 13-18 June.
Victims have told police he asked them sexual related questions, made sexual demands and was seen performing lewd acts.
Investigators have released a facial composite of a man they believe may be able to assist with their enquiries.
Investigators are keen to speak to any other person who may have had similar encounters over the past few months in this area.
Anyone who recognises the man, or has information that could assist police with their enquiries is urged to contact Crime Stoppers on 1800 333 000 or submit a confidential report online at www.crimestoppersvic.com.au