A Melbourne man has been fined $11,000 over the death of a four-year-old girl who was attacked by a pit bull terrier last year.

Lazor Josevski, 58, of St Albans, pleaded guilty to four charges over the death of Ayen Chol, 4, who was attacked and killed inside her own home by a neighbour's pit bull terrier.

The dog, which had no previous history of being violent, escaped from the backyard of Josevski's home when the roller door on his garage failed to close.

The animal attacked three people outside the house and was beaten off with a handbag. But it followed a young child inside and mauled Ayen Chol as she grabbed her mother's legs.

Josevski pleaded guilty to charges of owning a dog that attacked and killed a person, two counts of owning a dog that caused serious injury and owning an unregistered dog.

It was the first time Josevski has appeared in court to face the family. He was minding the dog for his son, who was overseas.

The magistrate said it was an example of how a relatively minor breach of the law can have enormous consequences.

He said the tragedy was beyond imagination and the family's pain was vivid.

The magistrate accepted Josevski's remorse. It was the first time Lazor Josevski showed up in court to face the family. ( ABC News )

Josevski was fined $4,000 for the death of the child, $6,000 for the two charges of causing injury and $1,000 for having an unregistered dog.

In a victim impact statement read to the court, the child's mother Jacklin Ancatto, described the terrifying attack.

She said the dog bit the little girl's face and dragged her away refusing to release the child despite being hit and kicked.

"Witnessing my daughter being killed by this dog was the worst thing that ever happened to me," she told the court in a statement.

Her father Mawien Chol Monjang told the court in his witness statement that he had never even heard of a child being mauled by a dog before.

Josevski's lawyer, Rob Stary told the court his client had written a letter of apology to the family before he was charged in which he expressed his sadness and regret over what he called a "horrendous" situation.

Under the Domestic Animals Act which was in place at the time of the death, Josevski can only be fined.

The law was changed in the wake of the death but was not made retrospective.

Now the maximum penalty for owning a dog that causes death is ten years in prison.