Simpson was sentenced to a minimum of nine years in prison for his involvement in a September 2007 attempt to reclaim what he thought was his property during a Las Vegas hotel room shakedown.
The court rejected Simpson's claims of prosecutorial misconduct during the trial, finding no truth to his claim that prosecutors elicited testimony by intimidating a witness, the Las Vegas Sun reported.
The court ruled, however, that Clarence Stewart, who was convicted with Simpson, should have been tried separately and ordered a new trial.
Simpson, 63, is serving time at the Lovelock Correctional Center. Stewart, 56, is at Carson City's Northern Nevada Correctional Center.
Simpson was acquitted in 1995 of his ex-wife's murder and that of her friend, but held liable in a civil suit for their deaths in 1997. His NFL pension protected by law, Simpson has paid little of a $35.5 million judgment.
Notable deaths of 2014 [PHOTOS]