This paper considers a low carbon supply chain consisting of a single manufacturer and a single retailer under the condition that the demand is uncertain. We first establish three games, including manufacturer Stackelberg (MS), retailer Stackelberg (RS) and Nash according to the different power structure of the firms. We then determine that the equilibrium stocking factors, emission reduction levels, wholesale prices and retail prices for the three models, respectively. After that, we demonstrate the effects of power structure. Results show that when the power shifts from the retailer to the manufacturer, the stocking factor decreases, whereas the wholesale price increases. Finally, we discuss the impacts of the random demand. We find that the expected profits of the firms, the emission reduction levels and the retail prices are increasing with respect to the market potential and low-carbon sensitivity coefficient, respectively. Meanwhile, they decrease with respect to the price sensitivity coefficient.