The Norfolk and Norwich University Hospital is launching a 'smoke patrol' to remind people that the habit is banned on its grounds.
It is hoped the move will improve the environment and save money - the trust spends £50,000 a year on cleaning and repairs associated with smoking.
People who smoke on the site can expect a tap on the shoulder to tell them about the ban and handouts on quitting.
Walkabouts by the hospital's Smoke Free Group will take place until Christmas.
The hospital's assistant director of nursing, Dawn Collins, said: "We want to make this environment for our patients and the public smoke free and as part of that we need to enforce it with our staff and contractors to enable this to be an environmentally pleasant site.
"We really want to get the culture of not smoking out of hospital exactly the same as the culture we have of not smoking in hospital."
Patrollers will wear high-visibility vests when they tour the hospital grounds at Colney.
The NNUH site was declared a smoke-free zone in 2005.