The case is among dozens before the Supreme Court during its January-February term. The Supreme Court has not scheduled oral arguments in the case.
In a post-conviction petition, an inmate argues he has found new evidence — or a possible constitutional issue — that could persuade a court to order a new trial.
The Supreme Court in 2001 upheld Grayson's capital murder conviction and death sentence.
Grayson, now 37, was convicted in George County in 1997. He was found guilty of the 1996 slaying of 78-year-old Minnie Smith during a house burglary. Authorities say Smith sustained more than 30 stab wounds on the night she died in her rural home at the edge of the Pascagoula River flats.
Court records show Grayson, who was arrested in Florida, had confessed to the crime, saying in a videotape that he entered the house through a window and intended to steal a gun to get money for drugs. He said he killed the woman when she woke up unexpectedly.
The Supreme Court denied Grayson's claim that he was coerced into confessing to the crime. He contended he had demanded an attorney while jailed in Florida and that demand should have followed him on return to Mississippi.
Prosecutors said Grayson signed a waiver of his rights and initiated the interviews in Mississippi and confessed not only in a statement but also on a videotape.
The U.S. Supreme Court upheld Grayson's conviction in 2005.