The court refused to hear Russell Henderson's claim that his state-appointed lawyers failed to discuss potential appeals with him.
In a deal with prosecutors to void the death sentence Henderson pleaded guilty to murder and kidnapping the gay college student in 1998. He is currently serving two life sentences.
Last month District Judge Jeffrey A. Donnell rejected Henderson's argument. Today's decision by the Wyoming Supreme Court lets Donnell's decision stand.
A second man, Aaron McKinney, was also convicted in the murder that galvanized the nation's gays. McKinney, also is serving two life sentences for the killing.
During their trial the court heard that Henderson and McKinney, both 21 at the time, kidnapped, pistol-whipped, robbed and left Shepard tied to a fence outside Laramie in October 1998. The 21-year-old University of Wyoming student died five days later at a hospital from massive head injuries.
The trial was told that the pair targeted Shepard solely because he was gay.