In the motion, Johnson said the life sentence on the kidnapping charge "was in conflict with the evidence presented at trial."
Johnson had said he did not believe he was guilty of kidnapping because he thought he had killed the Gaithersburg, Md., man.
Johnson had said he was high on crack cocaine when he attacked Donald Milligan, 50, of Gaithersburg, Md., on Aug. 2, 1996.
He later moved Milligan to the car's trunk and drove around while he and co-defendant Tammy Reel spent the night looking for crack cocaine, according to testimony at the trial.
He eventually threw Milligan into the Shenandoah River. Milligan, fearing for his life, said he played dead as his body was thrown in, not knowing if he would survive the fall.
"I just want the people to know there was no meditation to kidnap this man. We thought he was dead. We thought we were just hauling his body," Johnson said before he was sentenced to spend the rest of his life behind bars.
In the motion, Johnson also said that Reel received a much lighter sentence, but was as responsible for the offenses as he was. Reel, who testified for the prosecution, was sentenced to 20 years in state prison for her involvement.
Wheaton declined to answer questions about the motion on Monday. He also asked for additional time in preparing the appeal.
"There's been so much publicity on this case already, I'd rather not make a comment on it," Wheaton said.
Jefferson County Assistant Prosecuting Attorney Laurence Crofford, the lead prosecutor in the case, could not be reached for comment Monday.
No date has been set for when Wilkes will rule on the motions.