Fuzzy C-Means (FCM) clustering algorithm is sensitive to the initial clustering center and is easy to fall into local optimum. Therefore, a Firefly Fuzzy C-Means clustering Algorithm based on Levy flight (LFAFCM) was proposed. In LFAFCM, the random movement strategy of firefly algorithm was changed to balance the algorithm's local search and global search capabilities, the Levy flight mechanism was introduced during the firefly position update process to improve the global optimization ability, and the scale coefficient of each firefly was dynamically adjusted according to the number of iterations and the firefly position to limit the searchable range of Levy flight and speed up the convergence of the algorithm. The algorithm was validated by using five UCI datasets. The experimental results show that the algorithm avoids the local optimum and has a fast convergence speed.