The study shows access to sexual material online was top of the list of concerns for parents when it came to the internet.
Seventy-two per cent signalled access to such material was concerning, compared to only 30 per cent in 2007.
Forty-four per cent also expressed concern their children may accidentally access inappropriate material, compared to 22 per cent in 2007.
A lot of the concerns revolved around the challenge of monitoring children's online use, with parents being the key online content decision-makers for most children until the age of eight, when 59 per cent found the content for themselves.
Seventy- two per cent of Kiwi kids were also reported to be using the internet without any parental supervision.
But despite these concerns it seemed little had changed in terms of online filters to block access to unfavourable sites, with only nine per cent of parents having installed any such software back in 2007 and today.
Nevertheless despite these growing concerns, the research shows parents are taking other steps to protect their children.
Almost half had restricted the amount of time their children could have access to both television and online.
And the children themselves had greater awareness around what they should be watching, with almost half choosing to change the channel or close the browser when shown unfavourable content.
BSA chief executive Karen Scott-Howman said it was great to see parents proactively helping their children navigate their way through the media landscape.
"Challenging content cannot always be avoided in an environment where there is so much choice, so it's pleasing to see the majority of children know how to respond appropriately."
Read the full report online here: