Sgt Alex Blackman's legal team say he should have been convicted of the lesser charge of manslaughter.
His wife Claire spoke as documents were handed to the Criminal Cases Review Commission (CCRC) in Birmingham.
They include a pathology report which argues the fighter would have appeared dead when Blackman shot him.
During his trial at Bulford Court Martial in 2013 Blackman was known only as Marine A.
The 41-year-old from Taunton, Somerset, claimed he thought he was taking his anger out on a corpse, but was convicted of murder and lost an appeal in May last year.
Blackman's legal team argue the judge at the original court martial should have offered the alternative charge of manslaughter to the panel, the marine's repeated admissions that he had lost control and regretted his actions.
Speaking at a rally in Birmingham on Wednesday, Mrs Blackman said: "It's a strong application. There are a considerable number of new points of evidence or evidence of flaws in the original case, so we're cautiously optimistic."
The wife of a Royal Marine jailed for the murder of a wounded Taliban fighter says she hopes new evidence will help him secure a fresh appeal.