The survey, undertaken by SpectorSoft who make internet monitoring software, found that 22 - were worried about their kids accidentally accessing inappropriate content, and 17% said their youngsters had experienced cyber bullying.
And worryingly, over half the parents quizzed said they thought their children share too much information online, despite 735 of mums and dads talking to their children 'often' or 'quite often' about internet safety.
Senior director at SpectorSoft, Lisa Shaw said:
"Based on the survey data, there is little doubt that parents have their hands full as they seek to protect their children online. Parents are grappling with the vast amount of inappropriate content that their children can access via the Internet, as well as the threats posed by malicious individuals. Knowledge of their children's online activities is essential for ensuring their safety and teaching them to use the Internet responsibly and safely."
What do you think?
Are you worried about what your youngsters get up to online?
Have they - or you - suffered cyber bullying or sinister befriending?
Do you think we are generally too lax about about kids' internet useage?
More on Parentdish:
Despite these findings, nearly 2million still have NO access to the internet
Yet one in three kids has, shockingly, seen internet porn...