Graham was found guilty of the murder of Dale Watene at the end of a three-week jury trial before Justice Gerald Nation in the High Court at Invercargill in June last year.
She was sentenced in November to life imprisonment with a non-parole period of 13 years.
Yesterday, the Court of Appeal confirmed Graham had appealed her conviction and sentence.
At sentencing, Justice Nation said the killing and cover-up was callous and merciless.
Graham’s cover-up included telling one of her children Mr Watene was playing dead on the night in question, getting her friend George Hyde over to help first hide, then dispose, of Mr Watene’s body, pointing the finger at other possible suspects, digging Mr Watene’s grave with Hyde while her children played nearby and sending messages to Mr Watene’s mother Christine saying she would let her know if she heard anything about Mr Watene’s disappearance.
It was only at trial that Graham claimed the shooting was accidental. However, she was unable to recall who pulled the trigger.
The cover-up, she said in evidence, was because she was scared she would lose her children to Oranga Tamariki.
A hearing date has not yet been set for the appeal.