In this paper, a fuzzy bi-objective integer programming for a supply chain network design (SCND) problem considering stochastic transportation leadtime is proposed. The conflicting objectives considered in this study are maximizing the total net profit related to the supply chain network design and minimizing the probability of tardiness associated with transportation leadtime between manufacturing plant and distribution centers, and distribution centers and customers. It is assumed that possible risk associated with transportation leadtime follows a normal distribution with the established mean and standard deviation. The model was tested by varying risk levels in order to achieve the maximum satisfaction level in the network. By considering the acceptable satisfaction levels, analyzing the results of the proposed model will be providing different scenarios, which helps decision makers to have better insight to design the desired supply chain network. Results indicate that by decreasing the risk level, probability of earliness to deliver products to customers increases while profit decreases.