A man who strangled his elderly mother after an argument has been found not guilty of murder by a Sydney jury.

Instead, the Supreme Court jury found Terrence David Kain, 48, guilty of the manslaughter of his mother, Beverly Kain, in their Goulburn home on February 27, 2011.

Kain had pleaded guilty to manslaughter on the grounds of substantial impairment and this was accepted by the jury, who returned the verdict on Wednesday after one day of deliberation.

The court heard he strangled Ms Kain after an argument, before calling his sister and telling her, "Mum's dead. I strangled her. She's dead."

He told police at the scene he "just freaked out" and that his mother had blamed him for his father's death from cancer several years ago.

The jury was told Kain was an alcoholic, had suffered some brain damage as a result of his alcoholism and had a history of self-harm.

The trial heard medical evidence that Kain was mentally impaired at the time of the killing and his mind was "not working properly".

"His capacity, his ability to think properly, was impaired," defence barrister Peter Williams said.

The crown submitted that Kain knew what he was doing was wrong and intended to murder his mother or cause her grievous bodily harm.

Justice Michael Adams thanked the jury for their service, telling them, "There was ample evidence that justified that verdict".

Kain will be sentenced at a later date.