Last June, Jacques Delisle, 77, was sentenced to life in prison for killing his wife Nicole Rainville.
Rainville, 71, was found shot dead in the couple's Quebec City apartment in November 2009.
In 2009, Delisle told police his wife had committed suicide. The defense lawyer also argued the same thing at trial.
Rainville was partially paralyzed, having suffered a stroke two years earlier.
In court documents, Delisle's lawyer called the guilty verdict "unreasonable" and the trial "flawed."
Delisle unsuccessfully argued he should be out on bail pending his appeal.
He is believed to be the first member of the judiciary to ever stand trial on such a serious charge in Canada.
The hearing is due to last two days.