The Fifth U.S. Circuit Court of Appeals denied the appeal of John William King. He is on death row for his part in Byrd's death in 1998.
King argued his lawyers insufficiently presented his case.
Byrd was killed in Jasper by three white men allegedly because he was black. He was dragged to death behind a pickup truck.
Lawrence Brewer was executed in 2011 for his part and Shawn Berry is currently serving a life sentence.
Byrd's murder led Texas to pass its own hate crime law in 2001.