Based on the three-stage Stackelberg dynamic game model, this paper considers how to make product quality control strategy in the three-echelon supply chain consisting of the manufacturer, retailer and customer in the case of retailer dual channel structure (traditional retail channel, internet channel) and manufacturer dual channel structure (traditional retail channel, a third-party platform internet channel). When there are two types of decision model (decentralized decision, centralized decision), we analyze the demand price elasticity, market share ratio, revenue sharing ratio and quality cost coefficient how to influence the product demand, product quality level, retail price and direct price in different channels, expected revenue functions of manufacturer and retailer, consumer surplus and product quality control strategy. We find that: First of all, the retail price and direct price are positively related to product quality level, and the product quality level is negatively related with the demand price elasticity in traditional retail channel and the demand price elasticity in internet channel. What's more, the retailers’ retail price in traditional retail channel will be higher than direct price in internet channel. Thirdly, in the case of centralized decision, the manufacturers' product quality level, retail price, joint expected revenue and consumer surplus will all rise, but the direct price will fall. Fourthly, when the manufacturer establishes the dual channel structure, i.e., entrusting the third-party platform to build the internet channel, the manufacturer's product quality level, retail price, direct price, expected revenue, and consumer surplus will all decline. Finally, we conduct the numerical example by Matlab 2018, which verifies the validity and credibility of our conclusions, and points out the direction for the specific application of the model in practice.