The move follows a survey which found that 70% of youngsters over the age of 10 had online access at home - and a quarter had seen potentially harmful material.
"It's important that children are protected from unsuitable websites," said Ivan Lewis, education minister responsible for young people and learning.
"Much has been done to ensure that children surf safely at school, but parents also want to be confident that the internet is used safely at home."
Research commissioned by the Department for Education and Skills (DfES) found that children were spending hours online without parental supervision.
More worryingly, the study found 80% of parents did not know how to use the security settings on their computers to try to protect children from reading unsuitable material.
The research, carried out for computer retailer PC World's Safe Surfing campaign, also found that two-thirds (67%) of children were more knowledgeable about computers than their parents.
The Safe Surfing campaign, which begins on 15 November, is a nationwide scheme to generate awareness about internet safety.
It will repeat the standard advice to children not to meet any strangers they have had contact with over the internet.
Filtering software
Parents will be advised to buy computer software that will block any unsuitable material.
But an evaluation by the Parents Information Network (PIN) - an independent group which tests software - indicates that although most products of this sort offer some level of protection, none can be relied upon.
So it says strategies for protecting children might involve the use of "filtering" software, but should also include agreements with children about online times, unsuitable content and unsafe contacts.
"Children will also need strategies to cope when the filtering software does not work or is not present," PIN says.
Free tools
PC World Marketing Director Peter Keenan said: "There are plenty of simple measures that parents can take to ensure their children are safe online, and many are available for free.
Study findings
52% spend more than five hours online
Two-thirds of that time is unsupervised
Eight out of 10 home PCs lack adequate safeguards against harmful material
Two-thirds of children more knowledgeable about PCs than their parents
"Our campaign is designed to give parents greater knowledge of the tools available to ensure safer surfing."
PC World is also partnering with Parents Online, a DfES initiative, and has the backing of other child safety charities and internet awareness bodies.
TV presenter Carol Vorderman, a Parents Online supporter, said: "Parents need as much information as possible to help them understand the benefits of using the internet but also the safety measures they can take to keep their children safe online."