Abdi Ahmed was last seen just after 3pm on January 31 walking down Nash Way, off Kenton Road in Harrow.
The 41-year-old is said to be vulnerable and to have “no cash, phone or wallet”.
PC Callum Watts from the Metropolitan Police’s missing persons unit said: “We have exhausted all enquiries, with no confirmed sightings, and due to the fact he has no traceable items on him, we are appealing for the public’s help.
“It is crucial that we find Abdi – he is vulnerable and needs to return back to the mental health facility to receive the care and support he needs.”
Abdi has been described as Black, 6ft 2inches tall and with short black afro-style hair. He is also said to walk with a “distinctive limp”.
The 41-year-old was wearing a navy blue puffer jacket, black trousers, and blue plimsolls with white socks when he went missing.
Police have said that anyone who sees a man matching this description should call 101, giving reference 24MIS004279. For any immediate sightings, dial 999.