California Governor Arnold Schwarzenegger has been struck with more bad news - a majority of his state's residents doubt they'll support him should he run for re-election, a new poll has found.

A survey by the nonpartisan Field Poll found that just 36 per cent of voters would vote Schwarzenegger if he runs again, while 56 per cent would not.

Schwarzenegger, who took on his political role in 2003, has yet to announce plans to seek re-election in November 2006.

A recent poll conducted by the Public Policy Institute of California found that close to 54 per cent of Californians disapprove of the action movie hero's performance as governor - almost double the 28 per cent a year ago.