According to an ABC Australia report, the New South Wales Police seek to apply new technology to the 30-year-old cold case.
Watch: The New South Wales Police press briefing
This it the first time in Australian history that a cold case of this nature has been reopened.
The bombing on December 23, 1982, at the office of the Israeli Consulate General in William Street, left two people injured.
Later that day, a second bomb went off in a car parked outside the packed Hakoah Club in Bondi.
The case was never solved, but the New South Wales Police said that new technological advanced may now help them along.
Scene of the 1982 explosion
"We are following a number of investigative leads in relation to advances in technology and also in relation to our modern-day techniques," Assistant Commissioner Peter Dein, who heads the Counter Terrorism Unit, said.
According to the report, the Israeli government has been contacted as part of the renewed investigation.
At the time attacks were linked to an international pro-Palestine terrorist organization.
Australian authorities initially charged a 31-year-old with the Bondi bombing, but the charges were later dropped by the New South Wales Attorney-General. Police believe the suspects are still living in Sydney.
Police say the threat of another terrorist attack still remains if the suspects are not caught.
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