Dansie was found guilty in December of the murder of his wife Helen, 67, by pushing her wheelchair into a pond at Veale Gardens, in the Adelaide parklands, in 2017.

He is due to be sentenced on Thursday with prosecutors calling previously for the 71-year-old to get a longer non-parole period than the mandatory minimum of 20 years.

In the Court of Criminal Appeal on Monday, defence counsel Greg Mead SC argued the guilty verdict, delivered by a judge alone, was unsupported by the evidence despite the judge finding it highly unlikely that Mrs Dansie's death was an accident.

"The evidence was simply insufficient to enable the judge to jump from the finding that an accident was highly unlikely to a conclusion that murder was proved," Mr Mead told the court.

He said the financial motive for the killing the Crown had advanced was also "tenuous".

Mr Mead said Dansie's actions immediately after his wife's death and his contact with police, including lengthy interviews and conversations, were "entirely how you would expect an innocent man to act".

Prosecutor Jim Pearce QC said while he did not concede there was "force" in the issues raised by the defence it was open for the appeal court to hear the argument.

Justice Trish Kelly agreed and listed the appeal to be heard in March.

At recent sentencing submissions, Dansie's son Grant said it had been a relief when his father was convicted.

"I'm glad that Peter Dansie has been finally found guilty after the despicable, cold and callous crime," Grant Dansie said.

"It was sickening to think how mum spent her last moments. I truly hope he receives the harshest sentence he deserves."

During his trial, the court heard Dansie told police he briefly climbed into the pond after his wife fell in, but got out to call triple zero.

He told an operator he tried to keep Mrs Dansie's head above water and manoeuvre her to the edge of the pond in an unsuccessful attempt to rescue her.

But prosecutors argued it was no accident that Mrs Dansie's wheelchair ended up in the pond, and that her husband's story was implausible.

In reasons for his guilty verdict, Justice David Lovell ruled that all four elements of murder had been proven beyond a reasonable doubt.

"To put it another way, I find that Mr Dansie, deliberately and with intent to kill Mrs Dansie, pushed her wheelchair, in which she was sitting, into the pond in the gardens," he said.

"As a result of that action, Mrs Dansie drowned in the pond."

Australian Associated Press