With about 90 percent of ballots expected counted Saturday, Initiative 1240 was passing with 51 percent of the vote - a 41,689-vote gap. There are about 315,000 ballots received statewide that have not been tallied. The initiative was losing in King County, the state's largest.
Washington voters have rejected the proposal four times since 1995.
If results hold, Washington would become the 42nd state to allow the public independent schools.
Supporters say the charter proposal would offer new choices for struggling kids and their families. Opponents say charters have a mixed track record in other states and they would take away money from regular public schools.