A recovering heroin addict who murdered his girlfriend's 12-month-old baby in the Melbourne suburb of Richmond has been jailed for 25 years.

Silas Leithead was found dead in his cot in May last year with bruising to his head, fractures to his skull, ribs and arms, and a lacerated liver.

The court heard Paul Ta Voung seriously assaulted the baby while the baby's mother Kate Leithead was out buying heroin.

He then wrapped the baby up and placed him in the cot before Ms Leithead returned.

The court heard evidence that Ta Vuong was getting frustrated with Ms Leithead because she took too long to get drugs.

According to a witness, Ta Vuong suspected his partner was having a sexual relationship with her drug dealer, which lead to him "playing rough" with Silas.

But in her sentencing remarks Justice Karin Emerton said the most likely reason for killing Silas was because he wanted to get back at Ms Leithead for getting him hooked on heroin again.

"You used this tiny, dependent and defenceless child to vent your anger towards his mother," she said.

The judge said Ta Vuong displayed no remorse and continued to maintain the death was accidental.

She sentenced Ta Vuong to 25 years jail, with a non parole period of 20 years.