Egyptian-born Abu Hamza al-Masri, 48, was jailed for seven years in February after being convicted on 11 of 15 charges he faced at a London court.
His lawyer, Edward Fitzgerald, asked three of Britain's most senior judges at the Court of Appeal in London for permission to challenge the sentence.
Hamza's conviction should be overturned because there had been "oppression" and "general unfairness" due to the time between the offence and the conviction, Fitzgerald said.
He also complained about the conduct of the police, prosecuting authority, security services and the home secretary (interior minister).
Hamza's London mosque was at the center of some of the most high-profile terrorism cases of the last decade.
Convicted "shoebomber" Richard Reid, who tried to blow up a an American Airlines flight in 2001 with explosives hidden in his shoes, attended the Finsbury Park mosque.
Zacarias Moussaoui, the only person convicted in a U.S. court in connection with the Sept. 11, 2001 attacks, also went to the mosque.
Although British police have never linked Hamza directly to any specific plot, they said his mosque acted as a base for militants. Hamza, who was not in court for Friday's hearing, has said he is a prisoner of his faith.
Washington indicted him on 11 counts including having a role in a 1998 kidnap in Yemen, trying to help al Qaeda set up a "terrorist training camp" in Oregon, and funding the group.
In the 1998 hostage-taking, militants captured 16 Western tourists, including at least one American. Four hostages died in a botched rescue.
Washington wants to extradite him to face trial while he is serving his British sentence.
The hearing continues.