After a marathon five days of deliberating, a jury has found Melbourne man Arthur Freeman guilty of murdering his four-year-old daughter by throwing her off the city's Westgate Bridge.

The 37-year-old threw Darcey Freeman off the bridge in peak-hour traffic on January 29, 2009.

He had been driving the little girl to her first day of school when he pulled his four-wheel drive into the emergency lane and asked her to climb into the front seat.

He then carried her to the railing and dropped her 58 metres to her death as his two sons, aged two and six, watched on.

In a police interview played to the jury, Darcey's six-year-old brother Ben said his sister "didn't even scream in her fall".

"I said 'go back and get her. Darcey can't swim'. But he kept on driving. He didn't go back and get her," he said.

Just moments before, Freeman had spoken to his ex-wife, who was waiting at the school to mark the milestone.

"Say goodbye to your children," he said. "You will never see your children again."

Within half an hour of throwing the girl from the bridge, Freeman had driven his two sons to the Federal Court complex.

CCTV vision captured him frozen to the spot and shaking, unresponsive to the hugs and attention-seeking of his boys who, finally, sat at his feet on the floor.

Court staff were forced to change the nappy of his youngest son as they waited for police to arrive.

Freeman had pleaded not guilty to murder on the grounds of mental impairment.

He made no reaction as the verdict was read out last night, maintaining the same appearance he had throughout the trial.

Some family members started to cry, while his former wife and Darcey's mother, Peta Barnes, remained calm and composed.

Women in the jury wiped away tears when they were thanked by Justice Paul Coughlan for their service.

He thanked everyone involved in the trial for handling a very emotional ordeal with great dignity.

Transformation

During a two-week trial, Freeman's state of mind at the time of the January 29 killing was scrutinised.

He underwent a transformation after his daughter's death. His clean-shaven, tidy and professional appearance was replaced with unkempt hair, a permanent furrowed brow and a thick beard.

Chief Crown prosecutor Gavin Silbert SC urged the jury to dismiss the expert diagnosis of the defence's sole witness, Professor Graeme Burrows, who testified Freeman was suffering a major depressive disorder, and possibly psychosis, when he killed his daughter.

Thirteen months after the event, Professor Burrows diagnosed Freeman as having been in a state of "fluctuating" dissociation, as if sleepwalking or hypnotised, at the time.

He was the only one of six psychiatrists who believed Freeman was psychotic, and the prosecution labelled the professor a "psychiatrist of last resort".

Two psychiatrists who testified on behalf of the Crown disagreed with Professor Burrows's diagnosis.

They told the court that if Freeman had been in a state of dissociation he would not have been able to get the children ready for school, drive through peak-hour traffic, hold phone conversations, or pull safely to the side of the bridge and put on his hazard lights.

Under the watchful eye of the jury and court reporters, Freeman gave little away. He showed emotion rarely, often holding back tears until after the jury had left the court.

But he broke down when forensic pathologist Dr Matthew Lynch described the injuries that Darcey suffered in the fall.

Freeman mopped his eyes and face with a handkerchief, often raising his gaze to the ceiling as Dr Lynch described brain, lung and chest injuries suffered by the four-year-old - the result of "a fall from great height".

On the same day, Ms Barnes took the stand. Freeman's expression hardened again.

With her family in court for support, a stoic Ms Barnes told the court Freeman had had trouble controlling his anger. She answered in structured yes and no answers as counsel led her through her evidence. Details of her divorce were not elaborated on, but she corrected Freeman's lawyers' continual reference to her "husband".

"He is not my husband," she pointed out with a swift hand gesture to the dock.

In his closing address, Mr Silbert asked the jury to consider Freeman's unkempt long hair and permanent blank expression.

He told the court that in January 2009 Freeman had been clean-shaven with short hair.

"Ask yourselves now why he adopts the Rasputin-like appearance of a mad monk?" Mr Silbert said.

Defence lawyer David Brustman called on the jury to consider why a man would commit a "truly horrible" crime.

"Very few cases could induce more prejudice ... There in the dock sits a man who flung a four-year-old girl, his own daughter, to her death," he said.

"Now, how bad does that get? Is this simply the face of pure evil?"

Mr Brustman argued the killing of the girl was done by a mentally impaired man rather than a father intent on punishing his ex-wife in the worst possible way.

Freeman will have a plea hearing on Friday and is facing the prospect of life in prison.

Justice Coughlan has indicated Freeman will be sentenced before Easter.