Nearly three quarters (72 percent) of parents monitor their child's social networking account, says TRUSTe.
The privacy services provider's 'The Kids are Alright' report also revealed 84 percent of parents are confident their teen is responsible when it comes to posting personal information on a social network.
Furthermore, more than four in five (86 percent) of parents claim they know how much time their teen spends on social networks while 80 percent know the types of photos their teen has posted on the site.
More than four in five (82 percent) of parents feel they should be able to delete information from their teens' accounts by contacting Facebook or other social networking sites.
Eight out of ten teens admitted they use privacy settings to hide content from parents or friends and one in five (18 percent) teens said they had been embarrassed by or disciplined for something they posted on Facebook.
More than two thirds (68 percent) of teens also said they had accepted friend requests from strangers.
Four in five (80 percent) of adults said they have a social networking account, with Facebook www.facebook.com being named as the most popular.
The majority of parents (60 percent) spend up to an hour a day social networking. Of those parents that social network, 86 percent are friends with their child and a third said their child was responsible for them joining the social network,
"The data clearly shows that parents place the utmost importance on their teens' online privacy and control of their personal information," said Fran Maier, president and executive chair at TRUSTe.
"But, protecting the privacy of teens on social networks is not easy as they can be technically adept, have strong motivations to connect widely, and don't yet have the maturity to look out for their long term interests. "
TRUSTe said it is ultimately a parent's responsibility to know what their kids are up to in the world of social networking.
"Even though teens may be more technically savvy, parents have the greater breadth of world knowledge and insight needed to protect their children."
TRUSTe advised parents to learn about social networking technologies first-hand, as well as explaining to teens that they should only post information they are comfortable with others seeing and discuss which information should remain private.