The Howard League for Penal Reform claims such a move will serve to better protect vulnerable children.
The report notes that, as of January 2009, there were a total of 144 Welsh children – 139 boys and five girls – in custody.
However, half of these children were locked up long distances from their families in English prisons.
The Howard League points out that the Welsh Assembly Government has "taken big strides" to work on prevention rather than detention and says such a rights-based approach should be continued if devolution were to occur.
Elfyn Llwyd MP of the nationalist Plaid Cymru party, which forms a coalition Welsh government alongside Labour, described custody figures in Wales as "disturbingly high".
"This report echoes what Plaid has advocated for some time," he said. "Devolving the youth justice system would allow Wales to draw on best practice from across the world and set us apart.
"The devolved youth justice system is already working much better in Scotland for example. There is no reason why Wales should not take the lead too in being able to reform its own."
The former chair of the Youth Justice Board Rod Morgan has been commissioned by the Welsh Assembly Government to carry out a review on the possibility of devolving the Welsh youth justice system.
He is due to report by the end of the year.
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Charity supports moves to devolve youth justice in Wales
A report from a prison reform charity has backed moves to devolve the youth justice system in Wales.