The survey, conducted on August 8-13 among 570 Conservative members, showed that former UK Chancellor of the Exchequer Rishi Sunak enjoys only 39% support, while 61% said they were going to vote for Truss.
Outgoing British Prime Minister Boris Johnson still enjoys strong support among Tory members, according to the Opinium poll.
Asked to choose between Johnson remaining the prime minister or Truss taking over, 63% of Conservative members said they would prefer Johnson. Asked to choose between Johnson and Sunak, 68% said they would prefer Johnson, while only 19% expressed support for the former chancellor of the exchequer.
British Foreign Secretary Liz Truss and Sunak are the two final candidates in the election race for the post of prime minister, which came after Boris Johnson announced his resignation on July 7. Johnson's successor will be announced on September 5.