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.
A key plank of the Crown's case used MRNA evidence to assert brain matter was found in one of Lundy's polo shirts, and that the brain matter must have come from Mrs Lundy. MRNA showed which part of the body cells came from while DNA - which was not present - showed who cells belonged to.
Lundy said the defence experts had testified that evidence based on MRNA was "not ready to be used in a forensic setting".
He said the judge hearing the case had focused on the area when summing up and gave the jury information showing how complex the science was.
"I say it is inappropriate and unrealistic to expect a jury to determine such complex issues of scientific dispute."
He said other evidence in his favour, including petrol consumption, had to be considered against the weight the Crown put on the scientific evidence.
Prosecutor Philip Morgan QC said the Crown's case was that testing on two stains on the shirt produced DNA that was one billion, billion times more likely to belong to Christine Lundy than any other person in New Zealand.
However, the defence said that was impossible to link the DNA to the stains on Lundy's shirt. The court was told it was not unusual for family members to carry DNA on each other's clothing.