A Christchurch man has been jailed for two years and nine months for shaking his three month old baby daughter.

Christopher Dean Matthews was sentenced by Judge Garry MacAskill in Christchurch District Court on Friday after earlier pleading guilty mid-trial to charge of causing grievous bodily harm with reckless disregard for safety and one charge of assault on a child.

Judge MacAskill said his daughter Caitlyn was admitted to hospital with seizures when she was gravely ill.

She was sent to Auckland's Starship Hospital with chronic subdural haemorrhages on both sides of her brain, and retinal haemorrhage.

She stopped breathing for a time, and now had significant permanent brain damage.

Judge MacAskill said it had not been proven who was responsible for the permanent damage, and Matthews could not be held accountable for her ongoing suffering.

He said there was an abuse of trust and vulnerability because of Caitlyn's age.

Crown prosecutor Kerryn Beaton said there were at least two occasions of Matthews shaking Caitlyn to quieten her.

Defence counsel Garry Collin said at the time of the assaults Matthews and his partner were in financial difficulty, and he was not getting many hours sleep between working and looking after the baby.

The Plunket nurse who was attending the baby said Matthews was a caring and concerned father, he said.

Matthews was a first-time father, slightly naive and inexperienced with children.

He had some emotional detachment, some anger and frustration and a short fuse.

His pre-sentence report put him at a low risk of reoffending, Mr Collin said.

He was upset at his daughter's current circumstances, and there was now a breakdown in all the family relationships.