Adnan Mirza was convicted last year of two conspiracy counts and seven firearms violations.
Mirza argued evidence at his three-day trial in Houston was insufficient and that statutes under which he was arrested in 2006 were unconstitutional.
The Houston Community College student also contended he didn't violate terms of his student visa because he didn't know it was illegal to possess a firearm. The 5th U.S. Circuit Court of Appeals rejected each argument Tuesday.
Three others arrested with Mirza for participating in training exercises around Houston for a holy war pleaded guilty or have been convicted.
