Michael Wade Nance says he prefers that over lethal injection because injection would cause him "excruciating pain" due to a vein problem.
His attorney filed a complaint arguing Nance's veins are hard to see and too narrow and that execution by firing squad is "swift and virtually painless," making it a better option.
Nance was convicted in the 1993 murder of a man after robbing a bank.
He was sentenced to death in 2002.
Nance's appeals are in their final stages.
He must submit filings to the U.S. Supreme Court by Feb 12.