Issues pertaining to quality are of great importance in organizations and in the supply chain as well. A growing number of organizations have realized the importance of quantifying costs associated with product quality and optimizing their supply chains based not only on operational and logistics costs but also on quality-related costs or cost of quality. Therefore, it is expected to the supply chain management to maximize simultaneously the quality level of the final products and profit and to minimize costs related to quality, logistics, and operations. In addition, Nowadays, development of rapid accessibility to information technology has changed purchasing behavior of customers, So manufacturers have encouraged to sell their goods directly to customers along with the traditional sales. The dynamic and complex nature of supply chain imposes a high degree of uncertainty in supply chain planning decisions and significantly influences the overall performance of the supply chain network. In fact, with regard to changes in the economic environment, parameter related to the dual-channel supply chain network such as customer demand are variable. Hence parameter of demand is considered fuzzy in the mathematical model. Also, with regard to the fact that lead-time in both channels is the most important, So lead-time for both channels have been considered in the model. By reviewing researches conducted on the topic of supply chain network It can be concluded that few researches have been done by considering the cost of quality and no considerable research have been done in the dual-channel supply chain network. The aim of this research is considering the cost of quality in the supply chain network design of double-channel along with the level of quality constraint and lead-time constraint for both channels, as well as taking into account the demand parameters in fuzzy form. The mathematical model presented in this study is an MINLP problem. According to the proposed mathematical model, the problem is NP-hard and solving it in large scales need too much time. In order to solve this problem, two meta-heuristic solving methods based on genetic algorithm and simulated annealing algorithm has been used and their efficiency has been studied. In order to examine each of the proposed algorithms, Altogether 120 samples consisting of small, medium and large scales were solved and in small scales obtained results of the proposed algorithms and GAMS software are compared together and in medium and large scales obtained results of the proposed algorithms are compared together. The computational results show better performance of GA algorithm compared with the SA algorithm to solve the problem. Finally, the proposed model compared with the model without the cost of quality and the level of quality constraint and the single-channel model without lead-time constraint respectively and evaluate the impact of cost of quality, two channels for the sale of products, the level of quality constraint and lead-time constraint in the profit.