Along with the trend of low-carbon development, the government adopts a series of measures to control carbon emissions. Here, in the case with constraint of carbon cap and both firms and consumers have low carbon preference, we study the firm production decision problems in a supply chain consists of three firms The latest-firm-dominant situation is discussed by using Stackelberg game and we obtain the optimal output and emission reductions by the converse solution method. It shows that the optimal reduction decision of a firm is to make its marginal emission reduction cost slightly larger than purchase the corresponding emission rights from the carbon transaction market. The emission reduction of one side in a supply chain will motivate the others in the supply chain. With the enhancement of consumer low-carbon preference, the sales price will rise and lead to profits rise of the whole supply chain, but not all firms are profits benefit. Based on the above analysis, we extend the model to n firms aims to make some guideline sense for supply chain firms launching cooperation in areas of emission reduction.