In the USC Dornsife/Los Angeles Times poll, 64 percent of respondents said they supported the measure, which Brown wants to put on the ballot in November. A third of respondents said they opposed the measure.
It would increase the state sales tax a quarter cent for the next four years and create a graduated surcharge on incomes exceeding $250,000, to be in effect seven years.
The increases would help raise money for schools and balance the state budget.
Brown revised his original proposal, which would have relied more on sales taxes, and the latest measure would rely more on revenue from high-income earners, the Times said. The governor had faced pressure from liberal activist and union groups, which had offered a competing proposal that has been dropped.
In the poll, 80 percent of Democrats said they approved of the measure to 38 percent of Republicans. Among independents, who comprise 20 percent of the California electorate, three of four said they supported Brown's measure.
The poll also found about half of the respondents said they approved of the job Brown is doing as governor, compared with 35 percent who said they disapproved and 15 percent who said they had no opinion.
The poll is based on responses from 1,500 registered California voters March 14-19. The margin of error is 2.9 percentage points.