Charles Rhines was convicted in the 1992 stabbing death of a doughnut shop employee in Rapid City.
The justices are not commenting on the decision. In addition to the U.S. Supreme Court, Rhines has also appealed his conviction to the state Supreme Court, which also upheld his sentence.
We reached out to the Attorney General's office to find out what's next for Rhines.
It says Rhines still has one appeal pending --a federal habeas corpus claim to the 8th Circuit Court of Appeals.
Rhines is one of three people on death row in South Dakota.
The other two are Briley Piper and Rodney Berget.
Piper was 19 when he and two other men killed Chester Allan Poague back in 2000.
He was first sentenced to death by a judge in 2001. But ten years later, after his earlier punishment was overturned, he was sentenced to death a second time, this time by a jury.
Berget is facing the death penalty for killing Correctional Officer Ron "R.J." Johnson during a failed escape attempt at the South Dakota State Penitentiary in 2011.
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The Supreme Court rejected an appeal from a gay death row inmate in South Dakota who says jurors were biased against him because of his sexual orientation.