According to Hitwise, the online competitive intelligence service, the increase is due to the launch two weeks ago of the site's music service, dubbed "Bebo Bands".
This is the first time Bebo has overtaken MySpace in terms of weekly visits. The news comes as Fox Interactive Media has signed a deal to use Googlesearch to direct traffic across its network of internet sites, including MySpace.
Bebo is the eleventh most visited site on the net, beating MySpace at number 12 and bbc.co.uk at 13.