According to the lawsuit, the independent record label claims the country star failed to provide a fifth and final album by an April deadline, which was the agreement in their contract.
McGraw's spokesperson claims the singer turned in "Emotional Traffic" last fall and that Curb is holding the album "hostage" in an attempt to keep the singer "perpetually" under contract.
However, the label contends some of the songs were recorded so long ago they violate terms of the deal.
Curb is asking a judge to force McGraw to turn in new material for a fifth album. They also want to bar him from signing with another label and nullify a 2001 agreement that eliminated a sixth record from McGraw's contract.
The Associated Press contributed to this report.