Nowadays, companies have to improve their practices in the management of green supply chain with increased awareness of environmental issues worldwide. Selecting the optimum green supplier is crucial for green supply chain management, which is a challenging multi-criteria decision making (MCDM) problem. Moreover, while evaluating the performance of alternative suppliers, decision makers tend to determine their assessments using linguistic descriptors due to experts' vague knowledge and information deficiency. Therefore, this paper develops an integrated MCDM model based on the cloud model and QUALIFLEX (qualitative flexible multiple criteria method) approach to assess the green performance of companies under economic and environmental criteria. For the introduced model, the linguistic terms, expressed in normal clouds, are utilized to assess alternatives against each selection criterion. A linear programming model is established to compute the weights of criteria with unknown or incompletely known weight information. An extended QUALIFLEX approach is proposed and used to select the most suitable green supplier. Finally, the proposed green supplier selection method is demonstrated by an empirical example of an auto manufacturer to confirm its rationality and effectiveness.