Police are cracking down on cyclists riding through Brisbane's Supreme and District Court complex, despite the site originally being touted as a thoroughfare for bikes.

Court staff have complained to police about near misses with speeding riders, and on Tuesday officers conducted an operation during which they stopped cyclists and made them dismount and walk across the precinct.

The court precinct was considered to be an important link for CBD cyclists in 2010.

Riding a bike is legal in the large square, and parliamentary documents from November 2010 show the precinct was considered an important link for CBD cyclists.

"The design of the public square allows future completion of the pedestrian and cycle link from the Kurilpa Bridge to the future pedestrian traffic link proposed over Roma Street to the Roma Street Parkland," a Public Accounts and Public Works Committee report said.