The selection of sustainable supplier is an extremely important for sustainable supply chain management (SSCM). The assessment process of sustainable supplier selection is a complicated task for decision experts due to involvement of several qualitative and quantitative criteria. As the uncertainty is commonly occurred in sustainable supplier selection problem and hesitant fuzzy set (HFS), an improvement of Fuzzy Set (FS), has been proved as one of the efficient and superior ways to express the uncertain information arisen in practical problems. The present study proposes a novel framework based on COPRAS (Complex Proportional Assessment) method and SWARA (Step-wise Weight Assessment Ratio Analysis) approach to evaluate and select the desirable sustainable supplier within the HFSs context. In the proposed method, an extended SWARA method is employed for determining the criteria weights based on experts’ preferences. Next, to illustrate the efficiency and practicability of the proposed methodology, an empirical case study of sustainable supplier selection problem is taken under Hesitant Fuzzy (HF) environment. Further, sensitivity analysis is performed to check the stability of the presented methodology. At last, a comparison with existing methods is conducted to verify the strength of the obtained result. The final outcomes confirm that the developed framework is more consistent and powerful than other existing approaches.