UK children can bypass filters put in place by parents to block harmful content, according to Ofcom findings.
The study found that 18% of 12-15-year-olds know how to bypass internet filters, while almost 50% can delete their browsing history and 29% can amend settings to conceal their browser activity.
Another 83% of eight to 11 year-olds believed they could stay safe online.
Culture Secretary Maria Miller said: "Parents have a central role to play in protecting their children, including by talking to them about how to stay safe online."
The report also revealed that parents feel their computing skills are far inferior to their children's.
About 44% said children aged between eight and 11 say their child knows more about the internet than they do, while the figure rises to 63% for parents of 12-15-year-olds.
The release comes not too long after an investigation by the BBC revealed that filters were blocking out sex education websites.