The report, which examined online behaviour, attitudes and security habits with a focus on cyberbullying, found it was a "very real" online danger because of the damaging effect on people's mental health.
It found that harm was split evenly between females and males - but more than twice as many Kiwi girls as boys had been bullied online.
It also said that one in six children admitted to causing another person to have a negative online experience.
Brenton Smith, who is Symantec's vice-president and managing director Pacific Region, said parents were in the dark about the issue with many unaware of whether their child is being harmed - or is harming others.
"Online safety requires a combination of open and ongoing dialogue and education between parents and children," he said.
"While two-thirds of the children surveyed said they spoke to their parents about their negative online experience, only 22 per cent stayed away from where they were bullied online." Children needed more information to be able to make informed decisions.
Netsafe chief executive Martin Cocker said his organisation was seeing an increase in serious cases of cyberbullying for both children and adults but they had few remedial options available.
"We also see a number of perpetrators who are aware of, and feel empowered by, the lack of controls and regulations in the online space."
He said there needed to be regulation to govern the way individuals and businesses use the internet.
"And then you need to educate users and businesses about those rules, and have the resources to enforce them."
Mr Cocker said New Zealanders were increasing their technology use and were more likely to have negative experiences unless more could be done to create safer online spaces.
A bill called the Harmful Digital Communications Bill, introduced by Justice Minister Judith Collins last year, is expected to be passed by the end of the year.
Its proposals include creating a specialised approved enforcement agency for cyberbullying complaints.
Top 5 tips for parents and children
1 Set aside time to discuss appropriate online behaviour and create age-appropriate "house rules" about how computers, smartphones and gaming systems are used at home
2 For parents, be a positive role model and be aware that children like to imitate your behaviour
3 Do not share private information such as passwords, name and address, phone numbers with people you don't know
4 If you are being harassed online, block the harasser and report the harassment to an adult such as a parent or teacher
5 Do not respond to the harasser/s online as this could encourage them to continue
