Reducing global warming will require enacting strong climate policies, which is unlikely to happen without public support. While prior research has identified varied predictors of climate change policy support, it is unclear which predictors are strongest for the American electorate as a whole, and which predictors are strongest for Democrats and Republicans. In a nationally representative sample of registered voters (n = 2063), we use relative weight analysis to identify the strongest predictors of public climate policy support. We find that, among registered voters in the USA, the five most important predictors of climate policy support are: worry about global warming; risk perceptions; certainty that global warming is happening; belief that global warming is human-caused; and general affect toward global warming. Collectively, these five variables account for 51% of the variance in policy support. Results split by political party indicate that pro-climate injunctive norms and global warming risk perceptions are the variables that differ most between Republicans and Democrats, accounting for significantly more variance in policy support among Republicans. These findings can inform policymakers and advocates seeking to build public support for climate action.