They are attempting to raise up to $50m (£47m) so they can resume the hunt for the aircraft which disappeared on 8 March 2014.
The Boeing 777 was flying from Kuala Lumpur to Beijing when it vanished with 239 people on board.
It is believed to have crashed in a remote part of the southern Indian Ocean but the largest search in aviation history has failed to find the main wreckage of the plane.
In January families of those on board reacted angrily when it was announced that the £133m operation to find the aircraft was being called off.
Details of the families’ plan for a private search were announced at a memorial just ahead of the third anniversary of the plane’s disappearance.
Jacquita Gomes, whose husband was a flight attendant on MH370, said that what happened to the flight “should not go down in history books as a mystery”.
In July 2015 part of the aeroplane’s wing was found on Reunion Island, and so far more than 20 objects either confirmed or believed to be from the jet have washed ashore on beaches in Mauritius, Mozambique, South Africa and Madagascar.
Analysts have been looking at how the debris has spread to see whether they can trace it back and significantly narrow down the search area.
Jiang Hui, whose mother was on the plane, discovered a piece of potential MH370 debris in Madagascar last year.
She said: “I thought it was very miraculous and fortunate when I found the piece of debris that day, but I thought it was useless because this sort of searching activity should have been done by the government.
“It should not be us, the family members, who should have been subjected to this pain, to go and face this cruel reality.”
Grace Nathan, whose mother Anne Daisy was on board, said: “We want the next phase of our searching campaign to be that we will continue to look for the plane.
“So if the governments do not resume searching, we intend to source our own experts and own assets to continue searching.”
A number of theories have been put forward about what happened to the aircraft including a fire on board, hijacking or terror plot, rogue pilot action and mechanical or structural failure.
A final report on the plane’s disappearance will be released this year.