Papyrus, set up to tackle young suicide, said the risk posed by pro-suicide websites was not being taken seriously enough.
The charity said the 1961 Suicide Act should be amended to make it illegal to publish such material on the web.
The government said it was looking at how rules could be tightened.
At the moment, the law says it is illegal to aid, abet, counsel, procure or incite someone to commit suicide, but to be successfully prosecuted the individual has to have knowledge and participated in the suicide.
The charity said it was aware of nearly 20 internet-related suicides cases in the UK in the last five years.
Papyrus said typing "I want to kill myself" into an internet search engine offers access to 5m sites, many of which give information on how to commit suicide or were chat-rooms where techniques are discussed.
A spokeswoman added: "The sites take no responsibility for the advice they give, do not identify themselves and generally create an atmosphere where suicide is normal, acceptable and to be encouraged.
"The fact is that it is illegal to groom a child to have sex, but not to kill themselves."
The charity said as well as changing the law, the Department of Health's National Suicide Strategy needed to be amended to include reference to the dangers of the internet.
It also wants to see computer manufacturers and retailers include leaflets the charity has produced warning of the dangers of the internet when they sell products.
The Home Office said it was considering whether the 1961 Act could be changed to take internet sites into account.
But a spokesman said: "It is a very complex issue, as many of these sites are hosted abroad and UK law won't apply there."
And the Department of Health said it was looking at other ways of addressing the problem.
"We share the public's concern about these websites and the influence they can have over vulnerable people, particularly young people.
"Ministers are working closely with the Samaritans and the Internet Service Providers Association to look at ways of supporting vulnerable people who may be accessing these sites."