"Most people seem to think that when it comes to Sharia law it's just about the penal provisions, but that's not that case," Mr Trad said.
"(The penal provisions) can't work here. No serious person would advocate them."
But he said adopting aspects of Sharia marital and inheritance law - in a dual legal system - would be an advantage, particularly for women.
"At the moment it can disadvantage Muslims here, particularly women, because if a woman gets divorced through the normal civil process that divorce is not recognised in Muslim countries," Mr Trad said.
"So they would still be considered to be married elsewhere."
Equally, Australian governments don't recognise divorce documents made by imams, the mosque and community leaders, Mr Trad said.
"These are all considerations that Muslims living in Australia face all the time and a lot of them support introducing these parts of Sharia law here," he added.
Dr Matthews also said he was not proposing the introduction of wider Sharia law.
"I don't think we are so unsophisticated that we cannot consider a multilayered legal system as long as it doesn't conflict with the existing civil system," he was quoted as saying by Fairfax.
There are about 340,000 Muslims in Australia, or 1.7 per cent of the population, Australian Bureau of Statistics figures show.
Published: 8th March 2010 | Source: NEWS.com.au