A man who deliberately shook his 5-month-old stepson because he was resentful the child wasn't his is guilty of murder, a jury says.

William Wakefield, 32, was this afternoon found guilty of murdering baby Lincoln Wakefield, by a jury of eight men and four women in the High Court at Wellington.

Upper Hutt baby Lincoln Wakefield was rushed to hospital on June 11 last year with fatal brain injuries. He died the following day.

Wakefield initially denied intentionally hurting the baby, but later admitted in a police interview he shook Lincoln because he wanted to hurt him, saying he was "gutted" the boy wasn't his, and that he didn't even want to look at him.

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He met Lincoln's mother when she was already pregnant.

Through the police interview, he said he wanted to love Lincoln, but struggled with the fact the boy did not look like him.

Prior to the trial, he pleaded guilty to manslaughter, admitting he did kill the baby but denying his actions amounted to murder. He has also pleaded guilty to wounding with reckless disregard for safety, over an incident some weeks before Lincoln's death where he shook him and hit his head.

In the murder trial, which began last week on Tuesday, the jury watched the police interview with Wakefield, where he initially said he accidentally dropped Lincoln while bathing him.

Later in the interview he admitted the truth.

"I shook him first, not on purpose, and then I shook him again and then I shook him again ... to hurt him, I didn't mean to kill him," he said.

"I was in my own stupid world, I don't know why I did it. He's just not mine, it's hard for me to look at him."

The Crown said earlier Wakefield could still be found guilty of murder despite not intending to kill Lincoln.

To be guilty of murder, it said, the killer had had to intend to cause bodily harm to the victim, know such an action was likely to cause death, but consciously do it anyway.

Defence lawyer Steve Gill said Wakefield didn't fully realise shaking Lincoln would kill him, despite Wakefield's admissions in the police interview that he knew shaking babies could be fatal.

The jury delivered their guilty verdict today after about eight hours of deliberation.

Wakefield did not appear to show any emotion while the verdict was delivered.

Justice Robert Dobson convicted him and remanded him in custody to a date in July for sentencing.

Outside court, Detective Sergeant Rachael Boyd said she was "really pleased for Lincoln's family that Mr Wakefield's been held to account for this dreadful crime on a defenceless baby".

She said the verdict sent a strong message that people could be convicted of murder for shaking babies.

"It has been a difficult investigation for police staff involved . . . [it] takes a personal toll on staff, so I just want to acknowledge them.

"I've spoken to the family who are really pleased and grateful to the police for the outcome."