A northern Tasmanian man has been jailed for 21 years for the shaking murder of his nine-week-old daughter.

Brett Andrew Kitchin sat calmly in the dock and showed no emotion as the details of his attack on his baby daughter were read to the court.

Justice Helen Wood described it as "severe and sustained violence".

The court heard the then 26-year-old had been excited when he found out his partner was pregnant and had sought counselling so he could be a drug-free parent.

Baby Azzali Dolcie May Thomson spent the first week of her life in hospital with breathing and feeding difficulties and needed a gastric tube to make sure she was getting enough sustenance.

The court heard Kitchin had learned how to feed his daughter and had been an active part of her care.

But Justice Wood said Kitchin had found things stressful when the baby came home.

He was working full time, and starting at 3:00am, and money was tight. His partner was sick so he had to take on the majority of household chores, as well as care for a sick child.

He had returned to cannabis use and stopped seeing his drug counsellor. At the time he killed Azzali was withdrawing from ice.

The court heard Kitchin had been educated in pre-natal classes about the correct way to handle a newborn but despite that and being continually warned about his behaviour by his partner, Kitchin had treated the baby roughly.

Justice Wood said he had screamed in her face when she cried, wrapped her too tightly, bounced her violently in her bouncer, pinched her legs causing bruising when she would not feed and thrown her up in the air.

Father had duty to 'protect and nurture' the baby; Justice

Four days before his final attack on the child, Azzali's mother had taken her to their GP because she seemed unwell.

The GP advised her to give the baby paracetamol because she seemed to have a fever.

They did not know that Kitchin had squeezed the child so tightly around the chest that he had fractured four of her posterior ribs.

Kitchin had got up early to feed the baby but when she would not feed he became enraged, shaking her so hard he caused massive head injuries.

The court heard he thought that the baby was "just dazed" when he put her back into her bassinette and went back to sleep.

"[It was] an appalling act of violence and must be viewed very gravely," Justice Wood said.

"[It was] an act of severe and sustained violence. His moral culpability is substantial .... she was utterly defenceless and pitifully vulnerable.

"His duty of care was to protect and nurture his daughter."

Justice Wood said when Azzali's mother woke about an hour later she heard "a terrible scream she had not heard before".

She was unaware of the attack and when the baby kept screaming took her to hospital.

Azzali was airlifted to Royal Hobart Hospital but the injuries were too severe and she died.

Conviction result of voluntary confession by father

The court heard Kitchin had originally told medical staff and police he had accidentally knocked the child's head a few days earlier.

"The defendant well knew that he'd lost control on multiple occasions before while withdrawing from ice and that he was a real risk to his baby daughter while using drugs," Justice Wood said.

"[He] repeatedly breached his paternal obligation to his daughter."

Justice Wood also dismissed arguments made by Kitchin's lawyer that he was a new dad, inexperienced in parenting, and this was the result.

"This is not the conduct of a caring but ill informed parent," she said, pointing out that he had been taught how to handle a new born and had also been repeatedly spoken to by Azzali's mother about his treatment of the baby.

Six months after Azzali's death, Kitchin asked police to re-interview him about the death because he could not live with the guilt and confessed what he had done.

The court heard it was only as a result of that confession that Kitchin was charged and convicted.

Azzali's mother sobbed throughout the sentencing.

Kitchin was jailed for 21 years for the murder and an additional two-and-a-half years for the ill treatment.

He will be eligible for parole after serving 12 years and three months.

Kitchin's sentence will be backdated to when he was taken into custody after his confession in August 2014.