Moussaoui, who was spared from execution by the jury last week, is also appealing against a judge's refusal to let him change his guilty plea on six conspiracy charges. He made this latest appeal before the federal appeals court in Richmond, Virginia.
Earlier this week Judge Leonie Brinkema, who presided over his trial at a federal court in Alexandria, Virginia, rejected his attempt to change his plea.
Moussaoui had denied that he had any role in the attacks plan, and said he had a change of heart because he had decided he could now get a now fair trial in the United States.
No surprise
Moussaoui launched his appeal while he waits for a transfer to a "Supermax" prison in Florence, Colorado where he will serve out his life sentence. Lawyers were skeptical that the new appeal would get far, "He's wasting his time," said Kevin McNally, lawyer from the Capital Defence Network.
"It's not a surprise. Anyone who gets a long prison sentence appeals. You can always try. And lawyers can be very creative," said Eugene Fidell, president of the National Institute of Military Justice.
"I think the chances are very slight, vanishingly slight. He is a very long shot," Mr Fidell said of the appeal.
But Jonathan Turley, law professor at the George Washington University, said that Moussaoui has grounds to appeal the sentence. Mr Turley called the court's denial of the Al Qaeda plotter’s request to represent himself at the trial "a very significant constitutional error".
Foreman speaks
The jury's foreman, a female math teacher who cannot be identified for security reasons, has told the Washington Post that a single juror spared Moussaoui from the death penalty. The foreman said that the jury voted 11-1, 10-2 and 10-2 in favor of execution on Moussaoui’s three charges.
A unanimous decision was needed in at least one of the charges for the death sentence, and that left the jury only with the life imprisonment option.
"I felt frustrated," the foreman told the Post, "because I felt that many of us had been cheated by the anonymity of the 'no' voter. We will never know their reason."
The foreman, who said she favored execution, said that Moussaoui's dramatic testimony, in which he said he was to have flown a plane into the White House with British "shoe bomber" Richard Reid, carried little credibility.
She also found the defence argument that Moussaoui was mentally ill unconvincing, although she believed that many of his actions were "bizarre".
"I think most of us found Moussaoui to be intelligent, smart, crafty and a great manipulator. Those were the comments that were frequently thrown around the table," the foreman said.
The foreman is the second Moussaoui trial juror to be interviewed by the Washington Post, the first – a male juror – said that most of the other jurors believed that Moussaoui’s role in the attacks “was actually very minor.”
That juror said he voted for life in prison even though he considered the Moussaoui to be "a despicable character."