By considering the lag effect of mitigation investment, the differential game models are developed for vertical cooperative mitigation in a low-carbon supply chain. By applying the differential game, the optimal strategy problems of emission reduction investment, promotion investment and pricing are investigated in the decentralized and centralized decisions, respectively. Also, the optimal sharing rate of manufacturers is given in the decentralized decision. The paper comparatively analyzes the optimal equilibrium strategies in the two decision systems. The results show that the emission reduction investment of manufacturers and promotion investment of retailers are higher in the centralized decision than that in the decentralized decision, yet the economic performance of the low-carbon supply chain can be improved with the help of centralized decision when lag time is less than a given threshold value.