The NSPCC has revealed that its counselling service had more than 34,000 consultations with children who talked about killing themselves in 2013/14, an increase of 116% since 2010/2011.
ChildLine says that most of the children were aged between 12 and 15 and their head Sue Minto believes social media is making the problem worse because it meant "young people are unable to escape from bullying".
"When I was a child you could go home, shut the door and you would have some escape and some release and a chance to pull yourself together again," she said.
"That doesn't happen for our children and young people. They live in a highly pressurised world where the internet never sleeps and even if they turn off their phone, it's still there waiting for them."
The figures come from a new report entitled On the Edge - ChildLine spotlight: Suicide which also says the highest number of consultations on suicide - either conducted on the telephone or online - were on Sundays and Mondays.
'Learn from what young people are saying'
From April 2013 to April 2014, ChildLine held 34,517 counselling sessions with children who talked about suicide. Six thousand of these children had told a counsellor they had previously attempted suicide.
ChildLine said six in every 10 counselling sessions for suicide involved 12 to 15-year-olds. The helpline added that it had received calls from young people for various reasons but suicide was the only topic in which it had seen a significant rise in the number of people coming forward.
There has also been an increase in counselling sessions for children aged 11 or younger - although they account for just 2% of all sessions.
One in three young people counselled about suicide also mentioned self-harm in 2013/14, an increase of 29% compared with 2012/2013.Figures from the Office for National Statistics (ONS) show that suicide rates for 15 to 19-year-olds remained broadly consistent between 2000-2012.
Founder of ChildLine Esther Rantzen added: "We must learn from what they are telling us, and persuade them not to feel fearful or ashamed to tell others of their feelings.
"The first step is to make sure that young people have sufficient support around them. And so our report offers a wealth of guidance to parents, carers and professionals on where to seek help and how to open up these critical conversations with young people."