Five judges at the Court Martial Appeal Court in London will review the case of Sergeant Alexander Blackman.
Blackman, of Taunton in Somerset, will watch proceedings via video link from prison.
His wife Claire and dozens of supporters are expected to attend the hearing, which is due to last three days.
Blackman’s case has been referred to the court by the Criminal Cases Review Commission (CCRC), the independent body that investigates possible miscarriages of justice.
The CCRC announced it had concluded that a number of new issues, including fresh evidence relating to Blackman’s mental state, ”raise a real possibility” that the Court Martial Appeal Court ”will now quash Mr Blackman’s murder conviction”.
Blackman applied for bail in December, pending his appeal, but the move was rejected by two judges.
The conviction challenge is being heard by Lord Chief Justice Lord Thomas, Sir Brian Leveson, Lady Justice Hallett, Mr Justice openshaw and Mr Justice Sweeney.
Blackman was convicted in November 2013 by a court martial in Bulford, Wiltshire, and sentenced to life with a minimum term of 10 years.
In May 2014, the Court Martial Appeal Court rejected a conviction challenge, but reduced the minimum term to eight years because of the combat stress disorder he was suffering from at the time of the 2011 incident in Helmand province while serving with Plymouth-based 42 Commando.
Blackman shot the insurgent, who had been seriously injured in an attack by an Apache helicopter, in the chest at close range with a 9mm pistol before quoting a phrase from Shakespeare as the man convulsed and died in front of him.
He told him: ”There you are. Shuffle off this mortal coil, you c***. It’s nothing you wouldn’t do to us.”
He then turned to his comrades and said: ”Obviously this doesn’t go anywhere, fellas. I just broke the Geneva Convention.”
The shooting was captured on a camera mounted on the helmet of another Royal Marine.
During his trial, Blackman, who denied murder and was known at that stage as Marine A, said he believed the victim was already dead and he was taking out his anger on a corpse.
He was ”dismissed with disgrace” from the Royal Marines after serving with distinction for 15 years, including tours of Iraq, Afghanistan and Northern Ireland.
Reporting restrictions remain in place which prevented contemporaneous reporting of details given during preliminary hearings, including the application for bail.
Journalists have been able to report the judgments given by the court at the conclusion of those hearings.