The Royal Liverpool Hospital is stepping up efforts to remove smokers from within the hospital grounds.
The site became smoke free following the introduction of a national smoking ban in July.
But despite this, the hospital entrance continues to be plagued by smoke from people standing outside to light up, bosses say.
Spokesman for the trust, Mike Barker, says it is effectively a form of anti-social behaviour.
BBC NEWS | UK | England | Merseyside | Hospital still 'plagued' by smoke