The Mercedes driver launched the competition on Instagram on Thursday, declaring he was "on the look out for a dope new layout that evolves my current theme and features the candy apple red in my existing design."
The 32-year-old Briton, who has 3.7 million Instagram followers, said he would meet the winning designer at one of the race tracks to hand over the prize of a full size signed replica.
Hamilton, the clear pre-season favourite following the surprise retirement of German team mate and world champion Nico Rosberg last month, has changed his helmet design several times over the years.
In his early days and at McLaren, he raced with a yellow helmet in tribute to his boyhood idol Ayrton Senna, the late Brazilian triple champion. That changed when he moved to Mercedes in 2013.
Under Formula One's regulations, a driver's helmet design must be substantially the same for the entire season -- to ensure drivers can be distinguished easily -- but one special version is allowed at a race of his choosing.
Testing starts at the end of February, while Mercedes are due to unveil the new car at Silverstone on Feb. 23 with the season starting in Australia on March 26.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
