Around 37% of children aged between eight and 15 years said they worry about money, although this figure has fallen back from 58% when the same question was asked last year, according to the research by Halifax.
Parents living in Scotland and the East of England are the least likely to think that their children are worried about money, according to the survey of more than 1100 children and more than 500 adults.
The survey found children living in London are the most likely to be concerned about finances while those living in East Anglia are the least likely.
Richard Fearon, head of Halifax Savings, said: "Our comprehensive survey has consistently shown children are very sensitive to their parent's money concerns, far more so than parents realise.
"One key way to help children is to show them how money works.
"Introducing them to good spending and savings habits at an early age can pay long-term dividends by helping them see the benefits first-hand, while good financial education is vital."
Financial education charity pfeg (Personal Finance Education Group) has been pressing for children to start being taught about finances when they are still at primary school.
From September, financial education will be placed on the national curriculum in secondary schools in England.