Large-scale natural disasters have occurred many times and led to social, economic and environmental consequences. In other words, natural disasters are a serious threat to sustainable development. Recently, sustainable modeling of disaster relief logistics has increasingly attracted attention. It is vital to take the economic, social, and environmental aspects into account in the disaster relief logistic problem to reduce the harmful effects of a disaster. The present study aims to develop a multi-objective mathematical programming model for designing a sustainable distribution network of emergency goods in disaster relief logistics. The key feature of this formulation being the fact that it explicitly considers the economic, social (deprivation cost) and environmental aspects of sustainability in the objective function. Considering the inherent uncertainty in this issue a robust fuzzy optimization approach is utilized to deal with the uncertainty. Further, multi-choice goal programming is used to solve the multi-objective model. Finally, a case study was conducted on Sari city, Mazandaran Province, to verify the model performance. In this investigation, the optimal number and location of distribution centers are determined such that the economic, social costs and the environmental pollution level are minimized, and each distribution center provides services concerning its particular capacity to a set of demand points with different types of commodities. Using the proposed model, decision-makers and managers are able to make strategic and tactical decisions with the least cost and time, and in relief planning can enhance the structure of distribution networks and inventory and reduce victims’,dissatisfaction.