A young father who was jailed after he "lost control" and violently shook his six-week-old daughter in frustration has had his sentence doubled, after an appeal court found the baby's crying did not reduce his moral culpability.

The man, who cannot be identified for legal reasons, was sentenced to at least two years' jail in December for assaulting his daughter twice, causing at least 15 fractures and a brain injury.

During his trial in the NSW District Court, a jury heard he twisted the baby's limbs and violently shook her while his wife was out of their Sydney house on two afternoons in July 2011.

According to court documents, during the first assault, the father "took out his anger over his financial woes and his frustrations generally on his six-week-old baby".

After initially denying he was responsible for the baby's injuries, the father, then aged 20, told police that, during the second assault, he was feeling frustrated and angry about money and was missing his extended family, who lived far away.