North-West man Simon Adam Johnstone, 25, pleaded guilty to one charge of ill-treating a child and three charges of assault on his partner.

The child later died in hospital of injuries, but authorities were unable to establish who inflicted the fatal injuries.

The ill-treatment began in late 2012 shortly after the child's birth, where the father punched the child to stop him crying, held the child around the neck, and also placed his hand over the child's nose and mouth until it could not breathe.

He also shoved the child's bottle down his throat in an attempt to silence him.

A community nurse found a seven centimetre bruise on the child, and Johnstone replied: "I punched him because he wouldn't shut up."

Johnstone strangled his partner while she was holding the baby until she collapsed and dropped him.

Yesterday in Hobart's Supreme Court, Chief Justice Alan Blow took into account Johnstone's difficult childhood, and his various handicaps to being a father.

Johnstone's sentence will be backdated from March 2013.