Skilling, serving a 24-year prison term, is asking the court to consider whether the federal "honest services" fraud statute was applied correctly. The justices already have two other cases on their schedule dealing with the honest services law, a favorite tool of federal prosecutors in white-collar crime and public corruption cases.
The law has been criticized as vague and unfair because the government need not prove, in some instances, that a defendant personally benefited from the alleged fraud.
Skilling also questions whether he received a fair trial in Houston following Enron's collapse.
A ruling in his favor probably would result in a new trial.
In January, the 5th U.S. Circuit Court of Appeals in New Orleans upheld the convictions, but ordered Skilling's prison term reduced.
Skilling is the highest-ranking executive to be punished for the accounting tricks and shady business deals that led to the loss of thousands of jobs, more than $60 billion in Enron stock value and more than $2 billion in employee pension plans after the company imploded in 2001.
Company founder Kenneth Lay also was convicted of conspiracy, fraud and other charges, but his convictions were vacated after he died less than two months later of heart disease.
The case, to be argued next year, is Skilling v. U.S., 08-1394.