Robert Copeland, 63, was last seen in Campsie Street, in Springburn, on Wednesday morning.
Despite extensive searches, officers have been unable to trace him and they are now appealing to the public for help.
Mr Copeland, of Hillkirk Lane in Springburn, requires daily medication which police say he does not have with him.
He is described by officers as being "quite distinctive" and he is 5ft 10in, of heavy build and walks with a slow shuffle.
Mr Copeland has grey hair and a goatee beard and he was last seen wearing a black hooded rain jacket, black trousers and white training shoes.
Inspector Kenny Darroch, of Maryhill Police Office, said: "Despite extensive searches there have been no confirmed sightings of Mr Copeland since Wednesday and there is now an increasing concern for his safety and wellbeing."
Police think Mr Copeland may have travelled to Shettleston on the day he went missing.
Inspector Darroch added: "We would appeal to anyone who has seen Mr Copeland to contact us."
Call police on 101.