Baby Cezar Taylor lived for only six months, during which time he was violently shaken twice and dropped on his bed, a court has heard.
James Allan Fredrick Hemana lived with Cezar and his mother and is now on trial at the High Court at Auckland, charged with the murder of Cezar.
He has pleaded not guilty but accepts that he shook baby Cezar and failed to provide the necessaries of life.
The Crown says Hemana acted out of anger, frustration and jealousy when he violently shook baby Cezar on two occasions. On another he is alleged to have hit the baby in the back of the head.
Dr David Montgomery examined baby Cezar when he arrived at Middlemore Hospital on July 23 when the baby's mother, Victoria Taylor, brought him in with severe brain injuries.
The baby died five days later.
He said he noticed bruising on the baby's thighs and forehead and a scan of the baby's head showed bleeding on his brain.
Dr Montgomery referred baby Cezar to Starship Hospital and called in police.
He also interviewed Ms Taylor.
"I asked: Could anyone have hurt the child non-accidentally?'. She said that was absolutely impossible because only her and her brother lived with the child.
He said Ms Taylor blamed the baby's bruised head on him falling forward while sitting up.
"It didn't make sense. Nobody would expect a baby of this age to sit unsupported.''
But the Crown says Ms Taylor had been told by Hemana not to mention his name and to say bruises on the baby's head were caused by bumps and falls.
In his opening, Crown prosecutor Josh Shaw said she later told police that it was Hemana who caused the injuries.
Mr Shaw said Hemana is alleged to have grabbed the baby by the front of his stretch-and-grow before shaking him.
"He violently punches him back and forth repeatedly before dropping him on to the bed.''
Mr Shaw said Hemana also picked Cezar up by one leg and again violently shook him before dropping him on the bed.
He said Ms Taylor, tried to intervene. Hemana is alleged to have told her: "I don't give a f***, b****. I'll waste all of yous''.
He said Ms Taylor described her son as a "very different baby'' after the two incidents.
Hemana's cousin visited the couple in the days leading up to baby Cezar's admission to hospital and took two pictures of the baby on her mobile phone.
"He was constantly vomiting, barely awake and his eyes would roll. He was referred to as `zombie boy','' Mr Shaw said.
Hemana's lawyer Steve Bonnar said his client admitted shaking Cezar but said he was not guilty of murder.
"He's done a terrible thing _ he's caused the death of a child.''
But he said Hemana did not know at the time that what he did was likely to kill the baby.
"I have no doubt this is the most hated man in the courtroom. The air is thick with prejudice but ... do as Her Honour has asked and keep an open mind.''
The jury of six men and six women is set to hear from 54 witnesses over the next two weeks.
January 21: Baby Cezar is born to 20-year-old Victoria Taylor.
May 21: Ms Taylor, her younger sister and James Hemana move in to a house in Mangere
July 6: First shaking incident.
July 13: Second shaking incident
July 23: Baby Cezar admitted to hospital
July 28: Baby Cezar dies 10 minutes after life support is turned off. The same day, police locate and arrest Hemana.