Counsel for Danny McNamee, 38, argued that a convicted IRA terrorist was the likely source of many of the prints found on bomb-making equipment.
They said McNamee had served 11 years of a 25-year sentence for a crime he did not commit.
He was jailed in 1987 for conspiracy to cause explosions, which included the car bomb that killed four soldiers and seven horses of the Household Cavalry and injured 17 civilians.
Michael Mansfield QC, counsel for McNamee, said a false picture had been presented of his client at his trial as a "master bomb-maker".
Earlier this month McNamee became the first person convicted of a terrorist offence in England to be freed early under the Good Friday Agreement, when he was released from the Maze Prison in Northern Ireland. His case was the first to be referred to the Court of Appeal by the newly formed Criminal Cases Review Commission, set up to examine potential miscarriages of justice.
Yesterday Mr Mansfield told the court fresh evidence concerning a convicted bomb maker, Desmond Ellis, was now available, which undermined the prosecution case against McNamee and supported his defence. Ellis was the source of a "significant proportion" of the fingerprints found on devices with "explosive significance in the case against the appellant".
McNamee's conviction turned on the discovery of his fingerprints on tape found in two IRA arms dumps and on a battery that survived the Hyde Park explosion.
But Mr Mansfield argued that his client's work at an electronics factory where he would have been handling tape and repairing radios that contained similar batteries offers an innocent and more likely explanation for how his prints came to be found.
During the appeal, expert evidence will also be used to argue that the fingerprint recovered from the battery cannot be shown to be that of McNamee.
McNamee, from Crossmaglen, South Armagh, has eight grounds of appeal before the court. Mr Mansfield said the prosecution case against McNamee was "deeply flawed from the beginning".
Unusually, the IRA has issued a statement denying McNamee was a member of its terrorist organisation.
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