Considering a market consisting of a new energy vehicle (NEV) manufacturer, a fuel vehicle (FV) manufacturer, the government, and consumers with low-carbon awareness, this paper constructs NEV-FV competitive models to study the effect of greenness-based subsidy policy and dual credit policy on prices, quantities, profits, consumer surplus and social welfare. Under the greenness-based subsidy policy, the government provides subsidies based on NEVs’ carbon emission reduction to consumers. Under the dual credit policy, the FV manufacturer has to purchase NEV credits from the NEV manufacturer before starting to manufacture. The government’s optimal subsidy strategy and the two manufacturers’ pricing and production strategies of two kinds of vehicles are studied. The impact of consumers’ low-carbon awareness, NEVs’ carbon emission reduction, unit production cost, and unit cost gap between two kinds of vehicles with respect to equilibrium decisions are analyzed. The results show that both the greenness-based subsidy policy and dual credit policy can improve NEVs’ market share when the manufacturing cost gap is relatively low, and enhance the NEV firm’s competitiveness when the investment cost of greenness-enhancement is relatively low. The subsidy policy can improve social welfare, whereas the dual credit policy is harmful to social welfare. In terms of promoting the sales and profits of NEVs, both the subsidy policy and dual credit policy can play a positive role under different conditions.