With the rapid development of electronic commerce, consumers can freely buy the same product from a manufacturers’ Internet channel or a resellers’ physical channel. Based on the consumers’ channel preferences, this article classifies consumers into three types and investigates the price decision in a dual-channel supply chain using a Stackelberg game, which assumes that the manufacturer, as the game leader, first sets the wholesale price, then the reseller decides the retail price, according to the wholesale price. Furthermore, some numerical experiments are developed to investigate the impact of consumer acceptance, the degree of customer loyalty, and the proportion of identical shoppers on prices and profits. The results show that whether both the retail price and the wholesale price rise or fall depends on a combination of the cost of the physical channel and the Internet shopper’s acceptance of the Internet channel. The reseller’s profit is always lower than the manufacturer’s profit. The reseller’s profit is lower and the manufacturer’s profit is higher, compared with that of a traditional single channel supply chain. The numerical experiments showed that when an Internet shopper’s acceptance of an Internet channel is lower, the wholesale price and retail price in the dual channels will increase with an increase of the degree of customer loyalty (the proportion of identical shoppers). The reseller’s profit (the manufacturer’s profit) will reduce (rise) with the augmentation of the Internet shopper’s acceptance of an Internet channel. Finally, we design a revenue-sharing contract that can coordinate the supply chain and implement a win–win strategy for all partners. This work makes some contributions to the research area of coordination in dual-channel supply chains.