Around one in four children who called ChildLine Cymru/Wales last year had been bullied, the charity says.
The week aims to raise awareness about different types of bullying
It was the main concern for those calling the helpline, with 5,230 young people - 23% of all calls - asking for advice and counselling for bullying.
The figures, from April 2006 to April 2007, were revealed at the start of Wales' Anti-Bullying Week which is run by the Welsh Assembly Government.
This year's theme highlights the role schools play in dealing with bullying.
This will be the starting point for schools and others to explore cyber-bullying, safer routes for pupils, engaging parents and carers in school life, and racist and homophobic bullying.
Schools across the country will be holding events for students to highlight the issue, while staff will be briefed and workshops held for parents and carers.
Gemma Lang, who set up her own anti-bullying group Full Stop 2 Bullying after being bullied herself, said the week was important as it raised awareness.
"I think there are various reasons why so many people are calling ChildLine about bullying," said Ms Lang, who is also an ambassador for ChildLine Cymru/Wales.
"There are so many more forms of bullying these days. With new media they can get bullied at any time, in any place now.
"When I was bullied there wasn't the problem of cyber-bullies. Bullies now can be more anonymous which makes things more difficult."
ChildLine provides help to children suffering bullying
The NSPCC Cymru/Wales is using the week to call on head teachers to sign their school up to its new Defeat Bullying campaign, which gives teachers lesson plans to explore issues around bullying.
NSPCC schools' fundraising manager for Wales Gwen Axford said: "Teachers play a key role in stopping bullying, so it's vital that children feel confident about talking to their teacher and know that action will be taken."
Barnardo's Cymru has also published research which suggests problems could be reduced if more work was done with those who act as back-ups to a bully, and the passers-by who witness bullying but do not get involved.
Barnardo's research and policy officer Vikki Butler said: "Bullies tend to have groups of friends who do not carry out bullying themselves, but act as "back-up".
"Young people who take on this role are often scared of the bullies themselves, but feel they are protected from being bullied themselves by being part of the group."
Launching the campaign, Education Minister Jane Hutt said: "We must confront the issue in our schools and our communities and tackle bullying together, not just for one week, but for every week in the lives of our young citizens."