Snipes, 48, is best known for his work in the movies "White Men Can't Jump," "To Wong Foo, Thanks for Everything, Julie Newmar" and "Jungle Fever," as well as the "Blade" trilogy.
He was convicted last year of failing to file tax returns in 1999, 2000 and 2001 and began serving a three-year prison sentence in December. The actor has blamed his advisers for the lapse in payments.
CNN said Snipes did not immediately comment on the court's denial for his request for an appeal.
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