WA Police media spokeswoman sergeant Naomi Smith said the offences occurred between 9.45pm and 10.15pm when an armed man entered Eagle Boys in Willetton, a pizza store in Langford and then Pharmacy 777 in Langford.
On each of the three occasions, the man threatened staff with a firearm before stealing quantities of cash.
Ms Smith said it is believed that a second man might have been involved in the incidents also.
Police allege the fourth offence occurred when a 27-year-old woman was threatened by two men outside her home on Brookman Avenue in Langford.
One of the men pointed a firearm towards the woman, demanding she give them cash.
The men fled the scene after the victim explained she only had a small quantity of money.
Investigators would like to speak with the man pictured, who they believe can assist with their inquiries.
Anyone who can identity the man or provide further information, call Crime Stoppers on 1800 333 000.