A state appeals court two weeks ago rejected Spector's appeal.
Now the record producer's attorneys have asked the court to revisit its decision.
They suggested the court failed to consider that Superior Court Judge Larry Paul Fidler violated his neutrality by allowing the prosecution to show photographs of him among prosecution witnesses. They said this was coupled with a videotape of the judge explaining key forensic evidence.
Dennis Riordan, joined by fellow attorneys Charles Sevilla and Donald M. Horgan, alleged that jurors watched the tape during prosecution closing arguments, a move that turned the judge into a witness.
Spector was convicted in 2003 for the shooting death of Lana Clarkson.
Some legal analysts say the new request is expected to be denied and is just a first step toward an appeal with the California Supreme Court.
The Associated Press contributed to this report.