Fuzzy C-means (FCM) clustering algorithm is a fuzzy clustering algorithm based on objective function. FCM is the most perfect and widely used algorithm in the theory of fuzzy clustering. However, in the process of clustering, FCM algorithm needs to randomly select the initial cluster center. It is easy to generate problems such as multiple clustering iterations, low convergence speed and unstable clustering. In order to solve the above problems, a novel fuzzy C-means clustering algorithm based on local density is proposed in this paper. Firstly, we calculate the local density of all sample points. Then we select the sample points with the local maximum density as the initial cluster center at each iteration. Finally, the selected initial cluster center are combined with the traditional FCM clustering algorithm to achieve clustering. This method improved the selection of the initial cluster center. The comparative experiment shows that the improved FCM algorithm reduces the number of iterations and improves the convergence speed.