Sir Tim Berners-Lee told the BBC that those who "make life absolutely miserable" for women on the net should be named so they could be sued.
But he stressed offenders must be "judged by an open, accountable judicial process".
Sir Tim cited the Arab Spring as an case where social media anonymity was used as a force for good.
However, he warned that there needed to be a balance between the right to anonymity and the need to counter cyber abuse.
"Every society and every social network, every government and every country, is going to have to come to an arrangement, where perhaps people have anonymity initially - but there is a stronger force which can take it away."
Speaking at the World Economic Forum in Davos, Sir Tim, who created the first web page more than 25 years ago, dismissed calls from Republicans in the United States to restrict access to certain parts of the internet, in order to combat the rise of Islamic extremism.
"It's naive in lots of ways. Partly because you can't just prevent particular people from using the internet, partly because if people are planning an attack on the society - the fact that they are using the internet allows them to be caught as well."
"In some ways," he added, "law enforcement is easier on the internet than it is in real life."
The inventor of the world wide web has said there should be an option to disclose the identity of cyberbullies.