<p>With the carbon peaking and carbon neutrality goals, the coverage of carbon cap-and-trade mechanism is incomplete and the carbon price is low. The timely introduction of carbon tax policy and the construction of a carbon pricing synergy mechanism (carbon cap and trade with carbon tax) of "mainly carbon market, supplemented by carbon tax" can effectively guide areas not covered by the carbon market to participate in carbon emission reduction and improve the efficiency of green supply chain management. This paper discussed the coordination of two-stage green supply chain composed of a small supplier and large manufacturer and constructed the supply chain coordination game model under four decision situations. The results show that: (1) Levying carbon tax on the basis of carbon cap-and-trade mechanism can decrease the carbon emission in the supply chain, but cause profit loss. A certain degree of coordination can be achieved by further considering government subsidies and cost sharing contracts. (2) Carbon price, consumer green sensitivity coefficient, government subsidy rate, and cost sharing rate have positive impacts on decision-making. The government should scientifically and rationally subsidize enterprises with significant emission reduction effects and coordinate with supply chain contracts to give full play to the synergy of carbon pricing mechanism.</p>