Abstarct: Today, many industries are confronted with enormous competition and ambiguous environment, which has intensified due to technological innovations and changing customer needs. Agility paradigm is one of the ways to cope with such challenges. Studies have shown that in all literatures that addresses responsive supply chain design, maximum demand that can be met and delivery lead time have been cansidered as responsiveness criteria. In addition, in all researches, the customer demand’s dependency on delivery lead-time has been neglected. In this study, the design of a responsive supply chain network with delivery lead-time sensitive customers is investigated. The supply chain is multi-laxyer, multi-product and multi periods. The problem is formulated as a bi-objective optimization model that maximizes the net profit and minimizes the expected lead time. The proposed model is a mixed integer linear programming which is solved and analyzed with GAMZ. Also, it is solved with the ε-constraint method and produces a Pareto-optimal curve that reveals how the optimal net present profit, changes with different values of the Average Percentage of Non-Response to potential demand.. The application the proposed model is illustrated with a case study of petrochemical industry.