The movie, which is set in Texas and based on a critically acclaimed Cormac McCarthy novel, garnered four Academy Awards, including "Best Picture."
A message left for Paramount Pictures on Saturday was not immediately returned. Jones declined to comment through his publicist, Jennifer Allen, the San Antonio Express-News reported.
"The paperwork stands for itself," Allen said.
The lawsuit was filed Thursday in Bexar County in San Antonio. N.M. Classics, Inc., a Paramount subsidiary, is also named in the lawsuit.
Jones, who played Sheriff Ed Tom Bell in the film, claims he was not paid promised bonuses and had expenses wrongly deducted. The suit says Jones was paid a reduced upfront fee in joining the film, and that his contract had known errors not corrected before the movie was made.
Jones, 61, is asking that an auditor be named to review financial records to determine how much he should be paid.
