To ensure the continuity and stability of the supply chain under the sudden crisis, flexible supplier selection has taken up an important position in the operation decision of enterprises. Considering the differences of different expert decision-making and decision-making results that contain fuzziness, randomness and hesitation, the flexible supplier selection was studied by using the method of combining hesitant fuzzy language with normal cloud model and hesitant cloud linguistic term set was established. The weights were calculated according to the decision quality and aggregated with the evaluation results. Finally, WASPAS was used for scheme sorting to select the best supplier. The validity and applicability of the model were verified by a case study, which provided a scientific basis for enterprise decision makers to avoid interruption risk.