This paper focuses on the reduction of carbon emissions driven by cap-and-trade regulation and consumers' low-carbon preference in a dual-channel supply chain. Under the low-carbon environment, we also discuss the pricing strategies and the profits for the supply chain members using the Stackelberg game model in two cases. In the first (second) case where the initial proportion of consumers who prefer the online direct channel (traditional retail channel) is "larger", the direct sale price of low-carbon products could be set higher than (equal to) the wholesale price. And it is shown that in both cases, tighter cap-and-trade regulation and higher low-carbon preference stimulate the manufacturer to cut carbon emissions in its production process. However, improving consumers' low-carbon preference is more acceptable to the supply chain members. It always benefits the manufacturer and the retailer. In comparison, the firm's profit increases with carbon price only when the clean production level is relatively high. Our findings can provide useful managerial insights for policy-makers and firms in the development of low-carbon sustainability.