Lawyers fighting to save the life of a Victorian dog have told the High Court that the animal did not receive a fair hearing.

Izzy has been on death row since June 2013 after Knox City Council ordered the Staffordshire terrier be put down for biting a woman's finger.

Tania Isbester has taken her fight to save her dog Izzy to the High Court of Australia in Canberra. Credit:Melissa Adams

The victim suffered a 1.5-centimetre laceration when she attempted to stop Izzy attacking another dog.

Izzy's owner, Tania Isbester, has appealed the death sentence to the highest court in the land, arguing one of the decision-makers had been biased against the dog after being involved in court proceedings for the attack.