This is the first-ever Indian circumnavigation of the globe by an all-women crew.
The vessel is skippered by Lieutenant Commander Vartika Joshi, and the crew comprises Lieutenant Commanders Pratibha Jamwal and P Swathi, and Lieutenants S Vijaya Devi, B Aishwarya and Payal Gupta.
The vessel is likely to depart Fremantle on November 5.
Flagged off by Defence Minister Nirmala Sitharaman on September 10, the vessel has covered 4,800 nautical miles from Goa, crossing the Equator on September 17 and the Tropic of Capricorn on October 6, the Indian Navy said.
The vessel would return to Goa in April, 2018.
The expedition is being covered in five legs, with stopovers at four ports: Fremantle (Australia), Lyttleton (New Zealand), Port Stanley (Falklands), and Cape Town (South Africa).
The indigenously-built INSV Tarini is a 56-foot sailing vessel, which was inducted into the Indian Navy earlier this year, and showcases the 'Make in India' initiative on the international forum, the Navy added.