Richard Cummings, 85, was last seen by a friend at his home in Warwick Avenue, Maida Vale , on Saturday (April 9) at about 4.30pm.
Officers are concerned for his welfare as he has dementia, as well as limited mobility, and is likely to be confused.
He is not believed to have any money or his Freedom Pass with him.
He is described as white, 5ft8, of slim build, with grey hair. He might be wearing a camel coloured coat.
Mr Cummings is known to frequent South Wharf Road and the area around Warwick Avenue Tube station.
Anyone who has seen him is asked to call officers in Westminster via the non-emergency police number 101.