Considering the carbon emission quota and low carbon sales efforts in the dual-channel supply chain, the single period static game model and the multi-period dynamic game model are constructed to explore the optimal decision and the system stability respectively. In the static model, the optimal decision analytic formulas under the centralized decision and the decentralized decision are given. In the dynamic model, the local asymptotic stability conditions of the game system are explored, and the effect of delay parameters on the stability of the system is discussed. In addition, the instability system is effectively controlled. The study shows that the increase of carbon emission quota can increase the profit of the supply chain system; with the increase of low carbon sales efforts, the profits of the supply chain system and manufacturer will be reduced; the unreasonable delay parameter will lead to instability of the system.