A man convicted of the 2007 murder and rape of a 20-year-old deaf woman and the attempted murder and rape of another woman appealed his 26-year prison sentence today.

Liam James Reid was found guilty in the High Court at Christchurch of the attacks on both women, and jailed last December to preventive detention with a minimum non-parole term of 26 years.

He was convicted of the rape and murder of Christchurch deaf woman Emma Agnew and the rape, attempted murder, and robbery of a 21-year-old student in Dunedin.

The man, whom Justice Lester Chisholm called an "evil and dangerous predator", raped and murdered Ms Agnew at Spencer Park on November 15, 2007, and attacked a Dunedin student nine days later.

Reid raped the 21-year-old student and tried to strangle her before she belted him in the testicles and got away.

He denied all offending, saying he had been framed, and refuses to take treatment.

His lawyers appealed the conviction, saying vital DNA evidence was not provided in time to be properly analysed, Radio New Zealand reported.

They also appealed the previous decision, because Reid's prior criminal record was mentioned, which the judge then advised be disregarded.

Finally, the lawyers said the 26-year sentence was too long.

The Court of Appeal reserved its decision.

Ms Agnew's suffocated body was found hidden in forest scrub behind the Spencer Park camping ground, 15km northeast of Christchurch.

The profoundly deaf young woman had been missing for 12 days after texting family to say she was planning to meet a man who was interested in buying her car.

The Dunedin victim was walking home in the early hours of the morning when she was attacked in bushes beside a carpark in the central city.

She was punched, choked, threatened and repeatedly raped by Reid.