The blaze caused thousands of pounds of damage to Bishopbriggs Cultural Centre, in the town's Auchinairn Road, at about 02:20 on 17 November 2015.
The CCTV footage shows the man pouring liquid around and setting it alight.
He is about 5ft 10in tall and was wearing a blue tracksuit, a hat with an luminous rear band and dark shoes.
Det Con Stephen Cooke, of Police Scotland, said: "This was a deliberate and dangerous act which has caused extensive damage to the centre.
"I would appeal to anyone who recognises the man in the CCTV images to contact police as he may hold information vital to our inquiry."
Police have released CCTV footage of a man setting fire to a cultural centre in East Dunbartonshire that is used as a mosque by the Muslim community.