Supplier selection is one of the important processes in supply chain management. Regarding the emergence of sustainability issues in recent decades, companies have incorporated these issues in conventional supplier selection in order to meet governmental legislations and market demands. These issues have been noticed by various researchers. However, there are limited research activities which considered all aspects of sustainability for supplier selection problem as an integrated assessment. In this paper, an integrated approach of Fuzzy Analytical Hierarchy Process and fuzzy logic has been proposed in order to solve sustainable supplier selection problem. Fuzzy analytical hierarchy process has been used to calculate the weight of sustainable criteria and sub criteria. Then, fuzzy logic was utilized in order to assess the suppliers based on the weights acquired by Fuzzy analytical hierarchy process. Finally, a case study of petroleum industry has been carried out in order to show the validity of proposed approach.