Anthony McGinty, from Dumbeg Park in Wester Hailes, was spotted at the Lidl store in Nicolson Street at around 5pm on Thursday but has not been seen since.
The 28-year-old is described as white, medium build, 5ft 7in, with shaved red hair.
When last seen, he was wearing a black jacket, pin stripe trousers, boots, and elbow length satin gloves with a floral design. He occasionally wears a black tammy hat.
A police spokesman said that concern was growing for Anthony, and urged anyone with information about him to get in touch as soon as possible.
“We are growing concerned for Anthony’s safety and we are appealing to anyone who has any information regarding his whereabouts to contact us.
“He was last seen at the Lidl supermarket in Nicolson Street, and we are carrying out inquiries in order to try and establish his movements thereafter.
“He is known to frequent churches and shelters in Edinburgh that offer services for homeless people, and he is also known to walk extensively throughout the city.”
Anyone with any information is asked to phone police on 0131-311 3131.