With the booming of e-commerce, more and more industries open multi-channels. A supply chain model is studied in which both the manufacturer and the retailer introduce the e-channel in addition to the traditional physical channel. This model incorporates heterogeneous consumers' lower valuation of the product sold through the e-channel and the discounted prices available in these channels. Using the traditional single-channel supply chain as a benchmark, Stackelberg games are applied to obtain the optimal equilibrium solutions of the benchmark and the proposed model. The results show that, compared with the benchmark, the wholesale price and the profits and the manufacturer's ability to control the market all will be improved; the retailer will reduce the retail price when the proportion of demand for the retailer's Internet channel is less and vice versa, but her profits will always be less than that of the benchmark. The manufacturer's profits will be better with respect to his proportion of demand of the Internet channel; numerical experiments show that the retailer's profits may increase or decrease with respect to her proportion of demand of the Internet channel, which is influenced by discount rate and the consumer acceptance of the Internet channel. Numerical experiments further show that we observe that the manufacturer's profit will decrease (increase) with respect to discount rate (the consumer acceptance of the Internet channel), but the retailer's profit will increase (decrease) with respect to discount rate (the consumer acceptance of the Internet channel). The research has a guiding significance for the multi-channel supply chain pricing considering the discounted prices online.