A Northland man who murdered the mother of his two children by drowning her in a stream is appealing against his conviction on the basis he suffered a brain injury before pleading to the charge.

Jimmy Peter Akuhata has been serving a life sentence after pleading guilty to the 2012 murder of 21-year-old Ashlee Louise Anne Edwards.

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He was sentenced to life with a minimum non parole period of 15 years in 2015, but his case has reached the Court of Appeal four years later, on medical grounds.

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Akuhata was bashed by a "fight club" gang member drunk on moonshine while on remand at Mt Eden prison for Edwards' murder, leaving him with a brain injury.

He was declared fit to plead by the Court of Appeal before admitting the charge of killing Edwards.

Akuhata had four previous convictions for male assaults female, three of which involved Edwards.

Akuhata and Edwards had been in an "on again, off again" relationship for about six and a half years.

But when Akuhata murdered her, they were apart and there was a protection order in place for Edwards and her two daughters.

One night in July 2012, Edwards agreed to go to an event at a bar with Akuhata. During the night, he became angry at Edwards about text messages she had received.

According to facts accepted at the time, they left the bar about 1.55pm and were arguing on the Lower Tarewa Rd bridge when he lifted her up and over the railing into Waiarohia Stream.

He then grabbed her hair and held her head under the water until she stopped showing signs of life.

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He went home where he told a family member Edwards was dead.

In court in Wellington today, human rights lawyer Tony Ellis questioned Akuhata's previous lawyer, Catherine Cull, suggesting she did not try to run a defence for Akuhata and did not handle his case correctly, given his brain injury.

He asked whether there had been some pressure on "a brain injured person" to plead guilty.

But Cull said she had several discussions with Akuhata about the guilty plea and he was "keen" to enter it. She said she gave him plenty of time to think about it first.

Ellis told the panel of judges Akuhata didn't want to plead guilty to murder before the brain injury, and there must have been some type of pressure on him to do so.

He said cases like Akuhata's should be appointed one judge specially trained in dealing with "vulnerable defendants".

The judges have reserved their decision.