One British man is now thought to have gone down with the illness, after he flew back from Hong Kong.
But doctors in the UK say there is no need to panic. The man with the possible case in Britain is being treated at a specialist hospital with expert staff.
The only warning from some doctors is that people should think twice before travelling to the Far East at the moment.
Started in Vietnam
It's thought up to 200 people have been infected in the last week.
The disease may have started in a hospital Vietnam in February, when an American man died from it. Several staff caught the bug from him.