Martin Bush, aged 37, from Grove Place, Shelton, Stoke-on-Trent, has not been seen since October 10.
He was reported missing when he failed to attend an appointment.Mr Bush is described as white, 5ft 11in tall with a medium build.
He has short, dark brown, shaven hair and hazel-coloured eyes.He usually wears dark-coloured tracksuit bottoms, a dark jacket and a t-shirt. Over that a dark-coloured jacket over the top which is black or dark blue.
Mr Bush is believed to have access to a tent and has previously been found camping in the Staffordshire Moorlands.
A spokesperson for Staffordshire Police said: “We consider Mr Bush to be vulnerable and we are concerned for his welfare, especially during this current spell of bad weather.
“Extensive searches are underway to locate him and we would ask that anyone who has seen him, or had any contact, to get in touch.
“We would also encourage Mr Bush to contact us himself to confirm he is safe and well.”
Anyone with information is asked to contact Staffordshire Police on 101 quoting incident number 478 of October 15.