The Dutch-owned vessel Fugro Equator departed the Australian port of Fremantle on Monday (December 12).
It is scheduled to complete its scouring mission in the final search area of the Indian Ocean early 2017.
Officials have previous said they will suspend the investigation if the aircraft is not found by then.
The Fugro Equator has been part of a combined international search effort since the aircraft disappeared in 2014.
So far, not a single piece of wreckage or clues to the whereabouts of the aircraft have been discovered by the operation, BBC News.
Darren Chester, australian transport minister told the West Australian newspaper: "It has been an heroic undertaking but we have to prepare ourselves for the prospect that we may not find MH370 in the coming weeks, although we remain hopeful.”
Of course of the underwater search teams for a number of countries including Australia and China have taken part.
Earlier this month the Chinese vessel Dong Hai Jiu 101 completed its mission and is returning to Shanghai, leaving the Fugro Equator as the last ship scouring a 120,000 sq km (46,332 sq miles) search area.
Whether the Fugro Equator’s voyage is the ship’s final month-long deployment would depend on the weather, the office of Mr Chester told AP news agency.
MH370 was carrying 239 people when it disappeared en route to Beijing from Kuala Lumpur.