The case, Skilling v. United States, also raises the question of the scope of federal law that punishes a corporate executive's failure to provide "honest services," the Supreme Court Web site said.
A three-judge panel in New Orleans in July upheld Skilling's fraud conviction and ruled his trial was fair but should have been conducted outside of Houston, where sentiment against the company after its collapse ran high.
The nation's high court also agreed to hear a case addressing the scope of federal appeals courts' authority to overturn a conviction that could have been based on conduct that wasn't illegal when the crime occurred, the court said. Justice Sonia Sotomayor recused herself because she was on the circuit panel that heard the case earlier.
The court granted certiorari on a case raising the question of whether federal law on federal employees' health benefits pre-empts a state court lawsuit filed against a government contractor benefits administrator.
A fourth case the court agreed to hear takes up the issue of whether gross negligence by a state-appointed defense attorney in a death penalty case is sufficient to extend the time to file a federal habeas challenge.
The court took no action on a Guantanamo Bay, Cuba, detainee case that raised the question of whether federal judges can order the release of prisoners from the Uighur region of China into the United States.