Objective: The paper attempts to analyze the impact of institutional problem perception on the willingness of flexible employment workers to enroll in basic medical insurance, and to examine the explanatory role of medical insurance cognition. Methods: Based on questionnaire data from 1876 flexible employment workers, an institutional problem perception index and a medical insurance cognition variable were constructed. A Logit model was used for empirical analysis, and robustness tests were conducted by switching to a Probit model and adjusting the measurement of the core explanatory variable. Results: Institutional problem perception had a significant positive impact on flexible employment workers’ willingness to enroll in basic medical insurance, with an average marginal effect of 11.26 percentage points. Institutional problem perception also had a significant positive impact on medical insurance cognition. Dimension-specific results showed that perceptions of contribution burden, expected benefits, portability of social insurance relations, and information access all significantly affected enrollment willingness. Conclusion: The willingness of flexible employment workers to enroll in basic medical insurance is affected by institutional problem perception, and medical insurance cognition also plays a certain explanatory role. Enrollment willingness is closely related to various institutional links. It is recommended to optimize institutional arrangements in terms of contribution mechanisms, benefit expectations, transfer and continuation, and information services, so as to improve the adaptability of the basic medical insurance system to flexible employment workers.