The 37-year-old Frenchman, who was spared from being sentenced to 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.
The latest appeal of the only person ever tried in the United States for the 2001 attacks was made on Friday 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, outside Washington, rejected his attempt to change his plea.
Moussaoui had denied 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 fair trial in the United States.
No unanimous decision
Nearly 3,000 people had died in the suicide plane attacks on September 11, 2001 against New York and Washington, and Moussaoui, who was arrested a month earlier, admitted last year to joining a plot to fly hijacked planes into US buildings.
Nearly 3,000 people died in the
September 11, 2001 attacks
In the sentencing trial, which concluded on June 1, a 12-person jury had a choice between recommending the death penalty or life in jail without the possibility of parole.
The jury's foreman, a female math teacher, told the Washington Post that a single juror spared Moussaoui the death penalty
The foreman said the jury voted 11-1, 10-2 and 10-2 in favour of the death penalty on three terrorism 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.
The jurors spent 41 hours inside the small room in the Alexandria courthouse before reaching their decision.
Jury deliberations reached a critical point on April 26, the third day of discussions, the other jurors hoping that further discussions would identify the holdout, the foreman told the Post.
"It was as if a heavy cloud of doom had fallen over the deliberation room, and many of us realised that all our beliefs and our conclusions were being vetoed by one person"
The Jury's foreman
"It was as if a heavy cloud of doom had fallen over the deliberation room, and many of us realised that all our beliefs and our conclusions were being vetoed by one person," she told the Post.
"We tried to discuss the pros and cons," she said, adding that "most of the arguments we heard around the deliberation table" were in favour of the death penalty.
Brinkema, who handled the trial, ordered that the identities of the jurors be withheld for security reasons. The foreman contacted the Post and the interview was conducted on the condition of anonymity.
"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 favoured execution, said 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.
The defence argument that Moussaoui was mentally ill was also unconvincing, although many of his actions were "bizarre".
Moussaqoui will be shifted to the
Supermax prison in Colorado
"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 told the Post.
The foreman is only the second Moussaoui trial juror to be interviewed by reporters: on May 5, the Post interviewed a male juror who said the other jurors believed that Moussaoui's role in the attacks "was actually minor".
That juror said he voted for life in prison even though he considered the French Al-Qaeda conspirator as "a despicable character" and someone who "mocks and taunts family members whose loved ones died."
Moussaoui is the only person charged in the United States over the September 11 attacks. He is currently waiting to be transferred to a "Supermax" prison in Florence, Colorado.