Steven Wilson, 47, a restricted patient, failed to return from a period of unescorted ground leave at Leverndale Hospital near Paisley on Friday March 30.
A Scottish Government spokesperson said: "We are increasingly concerned about the whereabouts of a restricted patient who has been missing for over two weeks.
"Mr Wilson is 5' 8", slim build with receding black hair. He has brown eyes with a tanned complexion and he is clean shaven.
"He has a scar on the left side of his face which is 4" in length running from his mouth to ear.
"He has a tattoo of a cannabis leaf on his lower left arm and a tattoo of a love heart on the right forearm.
"He was last seen wearing a black t-shirt, red Adidas tracksuit top, blue jeans and white trainers.
"We are anxious to trace this man and if any member of the public see him they should contact Pollok Police on 0141 532 5600."