Mark Lundy's appeal focuses on scientific evidence that he says was too technical for a jury to understand.
The convicted double-murderer's appeal notice, obtained by NZME News Service, said he was also "considering the issue of unreasonable verdicts" because of evidence presented that contrasted the "inherent unreliability" of the scientific evidence.
Lundy was found guilty on April 1 of hacking to death his wife Christine and 7 year-old daughter Amber in their Palmerston North home in August 2000.
He was first convicted on 2002 but it was quashed by the Privy Council.
Lundy's appeal document stated the MRNA evidence - different from DNA evidence - should not have gone before the jury that found him guilty.