A man accused of smothering his wife of 41 years with a pillow was 'angry and jealous' of her involvement with a man from high school who she had reconnected with via Facebook, a jury has heard.

Warren Francis Rogers has pleaded not guilty to murder but guilty to the manslaughter of Anne Rogers, 61, in their Milperra home in September 2016.

His trial began in the NSW Supreme Court on Monday before Justice Julia Lonergan.

Crown prosecutor Nanette Williams said the court would hear evidence Rogers, then 68, confronted his wife over her 'ongoing contact' with the other man before the 'fatal conflict'.

Warren Francis Rogers has pleaded not guilty to the murder but guilty to the manslaughter of Anne Rogers (pictured) in western Sydney in 2016

Police found Ms Rogers dead in a bedroom and her husband 'semi-conscious' in a bathtub of red water.

The court heard when an ambulance officer asked Rogers what had happened he replied: 'She cheated on me four times. Stick a needle in my arm. I want to die'.

He later told police his wife 'asked him to kill her' so he smothered her with a pillow in the bedroom.

The couple separated for several weeks in mid-2016 but Rogers asked her to return 'when he was unhappy being by himself' on the condition she have no further contact with the other man.

'The accused was jealous and angry with the deceased because she continued, against his wishes, to have contact with (the man),' Ms Williams said on Monday.

The prosecutor said 'hand-in-hand' with that was Rogers' desire to maintain control of the family's finances including a $300,000 redundancy payout he received in the years preceding his wife's death.

'The accused would have been aware if the deceased left and went off with (the other man) ... there would have been a substantial redistribution of family assets.

'One way to prevent that, indeed, was to ensure that she didn't leave.'

Crown prosecutor Nanette Williams argued Anne Rogers' ongoing contact with the man caused arguments between the couple and shortly before her death, Mr Rogers told his wife to move out of their family home

The trial before Justice Julia Lonergan is expected to run for four weeks

Defence barrister Richard Pontello said Rogers was a 'true family man' whose behaviour was completely out of character.

He asked the jury to consider the defence of substantial impairment by abnormality of mind.

The marriage breakdown occurred 'in circumstances where Ms Rogers had been seeing another man she knew from her high school years, Mr Pontello said.

'After Mr Rogers learned of his wife's relationship ... he became very depressed. Very depressed indeed.

'(He) for all but one day of his 69 years lived with the highest degree of integrity and love for those around him.'

The lawyer said there was no dispute Mr Rogers caused his wife's death.

'However ... his capacity to control himself was in fact substantially impaired, arising from an underlying condition, namely the major depressive disorder from which he suffered and/or a chronic adjustment disorder.'