Gray is scheduled to be executed at 6 p.m. Tuesday at the state penitentiary at Parchman, Miss.
In court documents filed Friday, Gray contends his previous attorney didn't develop evidence of Gray's mental disability, an issue rejected by the Mississippi Supreme Court. The Mississippi court also rejected Gray's claim of mental disability.
Gray, now 38, was sentenced to death in 1996.
Gray was convicted for the 1994 slaying of 79-year-old Grace Blackwell of Louin. The woman's mangled body was found Aug. 15, 1994, at the end of a Newton County bridge.
According to the court record, Gray, in a jailhouse confession, told two cellmates that he kidnapped and raped Blackwell, shot her in the head with shotgun, tossed her from a car and ran over her with the vehicle.
An autopsy showed the woman had died from a shotgun wound in the head.
Blackwell was last seen alive after cashing a $1,200 check at her bank in Louin. Her car was later found behind a service station in Decatur.
Gray's execution, if not stopped, will be the second in Mississippi using pentobarbital due to a nationwide shortage of a different drug it has used in the past.
Benny Joe Stevens was executed May 10 using the new lethal drug mixture.
Corrections Commissioner Christopher Epps said after Stevens' execution that Mississippi officials had viewed executions in Oklahoma and Ohio where the new drug is in use.
"It worked out just as we were told," Epps said.
Mississippi has used a three-drug mixture for its lethal injections in the past, but one of those chemicals, an anesthetic called sodium thiopental, is in short supply. Sodium thiopental is one of the most common execution drugs used in the U.S., but the nationwide shortage has forced states to consider other options.