From the perspective of corporate social responsibility (CSR) of the e-commerce platform, this paper investigates the choice of e-commerce platform for wholesale sales, agency sales, and hybrid sales modes when the manufacturer has both an offline retail channel and an e-commerce platform channel. Taking the e-commerce platform as the dominant player and considering factors such as the potential market size of the e-commerce platform, consumers’ sensitivity to CSR input level, and the CSR input cost coefficient, we constructed a Stackelberg game model under the wholesale sales, agency sales, and hybrid sales modes. We explored the impact of the e-commerce platform’s CSR behavior on the choice of its sales modes as well as on the members of the supply chain. The findings indicate that, irrespective of the consumers’ sensitivity to CSR level and CSR input cost coefficient, the e-commerce platform tends to adopt the hybrid sales mode when its potential market size is smaller. Moreover, when the potential market size is larger, the wholesale sales mode is preferred; only when the potential market size is moderate, and consumers are less sensitive to CSR input level or CSR input cost coefficient is higher, the e-commerce platform will choose the agency sales mode. The increase in the potential market size of the e-commerce platform and the consumers’ sensitivity to CSR input level is conducive to the rise in the profits of the e-commerce platform, and the increase in the CSR input cost coefficient makes the profits of the e-commerce platform decrease. At the same time, the demand for the e-commerce platform increases as consumers become more sensitive to CSR input level or as the potential market size of the e-commerce platform increases. In contrast, the reduction in the CSR input cost coefficient negatively affects the demand for the e-commerce platform.