Kanye West's latest album has already been illegally downloaded more than half a million times, estimates Torrent Freak.
The artist released The Life of Pablo on Jay-Z's music streaming service Tidal two days ago.
Thousands of subscribers have complained that they have been unable to download the album, despite paying for it.
It is currently one of the most popular music downloads on The Pirate Bay.
The new material appears twice in the controversial file-sharing site's top 10 music downloads, despite Kanye West himself tweeting that it would only be available on Tidal.
The Recording Industry Association of America (RIAA) has also filed nearly 20 takedown requests to Google for websites illegally hosting the material, Torrent Freak reports.
However RIAA chief executive Cary Sherman wrote last year that the approach is increasingly ineffective.
"While the system worked when isolated incidents of infringement occurred on largely static web pages - as was the case when the [US copyright] law was passed in 1998 - it is largely useless in the current world where illegal links that are taken down reappear instantaneously," he said.
"The result is a never-ending game that is both costly and increasingly pointless."
The level of piracy of The Life of Pablo is unusual, Ernesto from Torrent Freak told the BBC.
"Generally we don't track music releases closely, so I'm not calling any records," he said.
"However, I haven't seen numbers this high before for a music release - not with Adele either."