This paper is devoted to the application of a class of differential games with continuous updating in low-carbon chain. It is performed that the optimal control (cooperative strategies) and feedback Nash equilibrium strategies uniformly converge to the corresponding strategies in the game model with continuous updating as the number of updating instants converges to infinity. With respect to the traditional model, this method gives the chances for players to adjust their strategies according to the information in the near future. The key point is that players could adjust their strategies corresponding to the current time information. In this paper we for the first time study the low-carbon chain differential game model with continuous updating.