With four months to go before the election, an initiative campaign to legalize marijuana for adults in California has a $5.5 million war chest.

Promoters of Proposition 64, the Adult Use of Marijuana Act, got a $2 million boost in donations this week from two key financial backers.

Sean Parker, who co-founded Napster and was Facebook’s first president, gave an additional $1.25 million, bringing his total contributions to $2.25 million.

The New Approach PAC, which is a legacy of Progressive insurance mogul and legalization activist Peter Lewis, gave an additional $750,000. The PAC has now contributed $1.5 million.

If approved by voters, the proposition will allow Californians 21 and older to possess up to an ounce of marijuana, up to 8 grams of concentrated cannabis and up to six plants.

Other backers of the initiative include Irvine-based Weedmaps; Drug Policy Action, the advocacy arm of Drug Policy Alliance, which aims to...