A CAIRNS Supreme Court Justice warned society would not tolerate violence against children in handing down a life sentence to man who raped and murdered a 14-month-old girl. 

Justice Stanley Jones said a life sentence had to be served for crimes that were "horrific, cruel and cause revulsion in all right-thinking persons".

"Violence towards a baby is something society can not tolerate," he said.

Following a two-day trial, a jury on Tuesday afternoon found Bradley William Logan, 20, of Palm Island, guilty of murdering the girl at a Cairns unit on January 15 last year.

Before his sentence was delivered, Logan pleaded guilty to two charges of raping the girl.

In his sentencing remarks, Justice Jones told the young man, who was 18 when he committed the crimes, that he was obviously angry and resentful at being left by the mother to look after the baby.

"You were also emotionally disturbed; the emotional state can be seen in the fact the day previous you had attempted to commit suicide," he said.

Justice Jones accepted Logan had shown remorse by pleading guilty to the rapes even though it had given little relief to the victim's family, some of whom travelled from Palm Island for the trial.

He said that in a victim impact statement, the child's grandfather expressed the feelings of the whole family when he said he "could not even put into words" how it felt to watch his family grieving.

"It has affected him in his work as an ambulance officer, particularly going to cases involving young children," Justice Jones said.

The baby's aunt, whose Westcourt unit was where the crimes occurred, described how she was now less trusting of people, over-protective of her own children and suffered panic attacks.

"And the mother; I don't think anyone can really understand the pain she will suffer because of your actions," Justice Jones said.

During the trial, it was revealed Logan inflicted repeated blows to the baby's abdomen that caused her to bleed to death internally, swung her by her legs so she struck her head on a TV and inserted objects in her body.

Logan was sentenced to life for the murder charge and eight years each for the two counts of rape, with the 582 days already spent in custody taken as time served.

No parole date was set.

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