In recent years, logistics development is considered as an important aspect of any country’s development. Outsourcing logistics activities to third party logistics (3PL) providers is a common way to achieve logistics development. On the other hand, globalization and increasing customers’ concern about the environmental impact of activities as well as the appearance of the issue of social responsibility have led companies employ sustainable supply chain management, which considers economic, environmental and social benefits, simultaneously. This paper proposes a multi-objective model to design logistics network for 3PL providers by considering sustainable objectives under uncertainty. Objective functions include minimizing the total cost, minimizing greenhouse gas emission and maximizing social responsibility subject to fair access to products, number of created job opportunities and local community development. It is worth mentioning that in the present paper the perishability of products is also considered. A numerical example is provided to solve and validate model using augmented Epsilon-Constraint method. The results show that three sustainable objectives were in conflict and as the one receives more desirable values, the others fall into more undesirable values. In addition, by increasing maximum perishable time periods and by considering lateral transshipment among facilities of a level one can improve sustainability indices of the problem, which indicates the necessity of such policy in improving network sustainability.