The British Heart Foundation survey found 54% children with parents who smoke worry about their health compared with just 34% for the offspring of non-smokers.
The foundation's Director of Communications, Maxine Smith, said: "Parents who smoke not only worry their children but are at much greater risk of dying prematurely.
"However, it is reassuring that health messages are getting through to children."
The study of children aged 10 to 16, carried out by NOP, found children from poorer, less educated families were far most likely to wish their parents took more care of their health.
It also found that 52% of children also think their parents should take more exercise.
The study forms part of a BHF campaign aimed at encouraging adults aged 25 to 50 to improve their lifestyles.
They say that in Britain more than 3,500 people under 50 die from heart disease compared with 2,200 from road accidents.
For your heart's sake - brush those pearly whites
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