A Sydney man allegedly smothered his wife to death with a pillow after she reconnected with a high school sweetheart on Facebook, a court has heard.

Warren Francis Rogers is on trial for the murder of his 61-year-old wife Anne in their Milperra home, in south-west Sydney, around September 12, 2016.

Prosecutor Nanette Williams told the Supreme Court jury Mr Rogers who was then 68, smothered his 61-year-old wife with a pillow on their bed after he found emails she exchanged with a high school sweetheart she had reconnected with on Facebook.

Ms Williams said Anne Rogers' ongoing contact with the man caused arguments between the couple and in July 2016 Mr Rogers told his wife to move out of their family home.

"At times they argued in front of others," she said.

Ms Williams said Mrs Rogers had been unhappy before her death and in August, she was admitted to hospital after a suicide attempt.

She said the retired couple had been married for more then 40 years and had two adult children.

The court heard that after allegedly smothering his wife Warren Rogers tried to take his own life.

He was found by police after family members raised the alarm when Mrs Rogers did not turn up for a birthday party.

The court heard Mr Rogers told ambulance officers who arrived at the scene that his wife was upstairs and he had killed her because she had cheated on him.

The prosecutor said Mr Rogers' state of mind at the time of the alleged murder was important.

She noted he had pleaded not guilty to murder but guilty to the lesser charge of manslaughter.

The crown has not accepted the plea.

"It is the crown case that he knew what he was doing because he was angry and jealous of her relationship," Ms Williams said.

"He also wanted to keep control of the family finances."

Completely out of character

Warren Rogers defence barrister Richard Pontello said it was a tragic story of the breakdown of a 40-year marriage.

Mr Pontello said Mr Rogers was a loving husband, father and grandfather.

He said Mr Rogers had been treated for various forms of cancer including prostate cancer before he killed his wife.

He said he was depressed and his capacity to control himself at the time of her death was "substantially impaired".

He said Mr Rogers' behaviour was completely out of character and he has no prior criminal convictions.

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