The jury verdict from 2011 provoked a torrent of outrage in Quebec.
Former cardiologist Guy Turcotte was granted his release from a psychiatric institution late last year — less than four years after the stabbing deaths.
The release prompted Ottawa to provide courts with new powers to lock up people found not criminally responsible for their crimes due to mental problems.
Turcotte admitted to stabbing his young children 46 times but said he didn't remember doing it, hadn't wanted to do it and had been experiencing blackouts on the night of the killings.
The Crown appeal of the verdict will be heard on Sept. 30 and Oct. 1.