With the development of economy and the improvement of people's living standard, health has become one of the most important things that people pay attention to. Lung cancer, as one of the most serious malignant tumors threatening people's health, has a high mortality rate and a low cure rate for the reason that the early symptoms of it are not obvious. Usually, when a patient is found to have lung cancer, s/he is already at the middle or even the advanced stage. The early screening of lung cancer is of great significance for the effective treatment of lung cancer. The lung cancer screening process can be seen as a multi-criteria decision making problem. However, the nature of making a right decision for lung cancer screening is unstructured and complex since there are many factors that may affect such decisions. Furthermore, these factors are usually vague and difficult to evaluate precisely and numerically. The hesitant fuzzy set is a powerful tool to deal with uncertain and ambiguous information and has better applicability in quantifying such information. This study establishes a framework that uses the double normalization-based multi-aggregation method to solve the lung cancer screening problem. The critical factors for lung cancer screening are obtained by the fuzzy Delphi method. We adopt an illustrative example that is related to the lung cancer screening in a hospital of China to demonstrate the effectiveness of the proposed model. Furthermore, a comparison analysis is provided to verify the stability of the proposed method.