Google pledged to take action against music piracy six months ago by taking into account how many copyright infringement notices it has received against them when it determines their ranking.
Google said at that time that sites with high numbers of removal notices might appear lower in our results, the Telegraph reports.
The RIAA claimed that Google's changes are not working, however, and known unlawful download websites still appear in the first page of results.
According to the RIAA's report, pirate websites such as mp3skull.com still appear more often in the top ten results for common music searches than licensed digital music retailers such as Apple and Amazon.
The organisation said Google has received more than 100,000 copyright infringement notifications against mp3skull.com, it said.
Google has yet not responded on the RIAA's criticisms.