Hamilton led new team mate Valtteri Bottas in a Mercedes one-two in the first session and raised the pace in the second to be comfortably quicker than Ferrari's second-fastest Sebastian Vettel on a cloudy day at Albert Park.
The Briton's fastest lap in the second session of one minute 23.62 seconds was more than half a second clear of four-times world champion Vettel, who edged Bottas into third.
Vettel's 2007 championship-winning team mate Kimi Raikkonen was fourth fastest in the final session, improving on his fifth placing earlier.
The first session was largely incident-free but a number of drivers suffered problems later, with Renault driver Jolyon Palmer having a particularly tough day.
Blighted by a seal problem in FP1, Palmer's second session ended quickly as he skidded out at turn 16 and slammed into a barrier, scattering debris on the track and raising a red flag until his wrecked car was winched off.
Read the full article on eurosport.co.uk: Hamilton and Mercedes throw down gauntlet