Matthew Milat, the great-nephew of serial killer Ivan Milat, will appeal against the 43-year jail sentence handed to him for the axe murder of 17-year-old David Auchterlonie.

The NSW Director of Public Prosecutions said it had received a notice of intention that the 19-year-old and his co-accused, Cohen Klein, would appeal against the ''severity of sentence''.

Milat was given a non-parole period of 30 years and Klein, also 19, was sentenced to 32 years with a 22-year non-parole period last month for the murder in the Belanglo State Forest in November 2010. It is understood the pair believe they should have been given discounts on their sentences because they both entered guilty pleas.

David's grandmother, Sandra Auchterlonie, said her family were disgusted that Milat would think he was entitled to a lesser sentence.

''We've started to get back to a bit of normality then he's gone and done this,'' she said.

''I'm shocked that they think about an appeal. They should have both been given life because we have been given a life sentence.

''I think what they are doing makes them cowards.''

Mrs Auchterlonie said the family were prepared to sit through further court hearings to ensure that justice is done for their grandson.

David was lured to Belanglo - the same spot where Ivan Milat killed seven backpackers during the 1990s - by the pair on the night of his 17th birthday to drink and smoke cannabis.

When the teenagers arrived at the southern highlands forest, David was tortured, tormented and then murdered with a double-sided axe by Milat.

His body was buried in the forest in what the Crown prosecutor Lloyd Babb, SC, called ''an adrenalin-fuelled thrill kill''.

In sentencing the pair in the NSW Supreme Court last month, acting Justice Jane Mathews said Milat remained a serious potential danger to the community. She rejected Milat's claims of remorse, saying he took the life of an innocent young man - who was unfortunate enough to be his friend - in an unimaginable, cruel, brutal and violent manner solely for his personal enjoyment.