Karl Hawkins, aged 43, from Southey Green, has not been seen since Tuesday, June 21, when he bought a mountain bike in Lincoln.
He left his home two days earlier.
Mr Hawkins has a medical condition, which needs treatment.
Detective Chief Inspector Pete Grayson, from Lincolnshire Police, said; “The safety and wellbeing of Karl is our only concern.
"I would appeal for anyone who knows or has seen Karl to get in touch. If Karl is reading this than please call and let us know you are safe.”
Mr Hawkins is 5ft 9ins tall and of a skinny build.
Anyone with information should call Lincolnshire Police on 101.