Most of the estimated 1.7 million victims of the 1975-79 ultra-Maoist regime died of starvation, torture, exhaustion or disease in labour camps, or were bludgeoned to death during mass executions.
Guilty verdicts have so far been reached against three former top members of the regime, but several have died while on trial or before indictments were made.
Khieu Samphan's defence team argued that the trial chamber in its verdict had failed to provide sufficient reasoning and violated its own legal framework.
Lawyer Kong Sam Onn told Supreme Court judges present at the hearing that they should dismiss the chamber's ruling.
"The judgement against Khieu Samphan has no legal effect, it should be null and void," the lawyer said, adding Khieu Samphan had been denied a right to a fair trial.
Co-prosecutor Chea Leang defended the 2018 judgement saying evidence for the conviction was "extensive, diverse and compelling."