Pham Trung Dung, 37, was caught with two suitcases containing the drugs at Tan Son Nhat airport in May last year while trying to return to Australia with his wife and children.
Dung told a court in southern Ho Chi Minh City that he had been promised US$40,000 (1.3 million baht) by two unidentified men to transport the drugs, an online report by the Tien Phong newspaper said.
Vietnam has some of the world's toughest anti-drug laws. Anyone found guilty of possessing more than 600 grammes of heroin, or more than 20 kilogrammes of opium, can face death.
Earlier this month, six people from a 25-member smuggling gang were handed death sentences for smuggling 620 kilogrammes of heroin and 1,400 ecstasy pills in northern provinces.
In January authorities sentenced 30 smugglers to death in the country's largest ever narcotics case, involving scores of defendants and nearly two tonnes of heroin.
Australian Foreign Minister Julie Bishop said the Foreign Ministry was working through diplomatic channels to provide assistance to Dung.
"Of course we do not support the death penalty in Australia ... we are providing consular support and advice," she said in comments to the Australian Broadcasting Corporation.
Australia's Department of Foreign Affairs said it understood he had the right to appeal.
"Whether he decides to do so is a matter for the man and his lawyers," a spokeswoman said.
According to media reports and an AFP tally, Vietnam has more than 700 prisoners on death row.
Many have been sentenced for drug offences including dozens of foreigners — although it has been decades since a foreign citizen was executed.