A mother has been found guilty of the manslaughter of her 13-month-old baby son.

She left him in a deep bath for at least 15 minutes and he toppled over and drowned. She has been on trial for murder after the Crown alleged she left him there on purpose because she couldn't cope with looking after him.

The jury reached the verdict at the High Court at Auckland tonight after deliberating for five hours.

The 29 year-old woman, who has name suppression, had no reaction when the verdict was delivered. She has been remanded on bail until sentencing September 28.

She had been charged with murder but was found guilty of the alternative charge of manslaughter. Her barrister, John Anderson, argued the death was accidental but invited the jury to find her guilty of infanticide if they considered she caused the boy's death.

Infanticide is a partial defence to murder where a mother can be found not guilty of murder because at the time of the killing her mind was disturbed because she had not fully recovered from giving birth.

The woman testified she thought the boy would be strong enough to sit by himself in the bath which she had filled with water almost to his shoulder height.

She went to the kitchen to make breakfast and about 15 minutes later "suddenly" remembered him.

"I went back into the bathroom and saw [baby]. He was on his stomach face down into the bath. I froze."

She picked him up and checked his pulse.

"He wasn't breathing, his body was quite heavy... His mouth was blue. I knew he was dead."

She didn't call 111 because she didn't want her husband to come home and see "the commotion". When he did get home she remembered being numb and in shock.

The Crown alleged she left the baby in the bath on purpose she couldn't cope with caring for both her children because she was "desperate".

The children had been in Child Youth and Family care but returned to her two days before the drowning on November 6, 2009.

Prosecutor Rachael Reed told the court: "She could not cope with both of her children and could see no way to solve the problem except for his death."

After the baby drowned the woman wrapped him in towels and blankets and went on her computer looking at Facebook profiles until her husband came home and she showed him the baby's lifeless body.

Ms Reed said the Crown case was she deliberately left the boy, knowing he was unsteady in the bath because she couldn't cope.

The court heard the woman had a traumatic childhood. Her mother burned herself to death, her aunt died after jumping from a building and her father died in a plane crash.

She said she had been raped three times when she was a young girl. When she learned her 5 year-old daughter had also been sexually abused in CYF care it bought back memories of her own abuse.