The initial clustering center and membership matrix of the traditional FCM algorithm are randomly selected, so if there are outliers or uneven distribution of the data set, the FCM algorithm will fall into a local optimum, which will affect the clustering result. In view of the above problems, this paper proposes an adaptive weighted FCM algorithm based on density peaks. This algorithm improves the FCM algorithm by two points: first, the algorithm uses the density peak idea of the DPC algorithm to determine the initial clustering center, so as to improve the shortcomings of the FCM algorithm to randomly select the clustering center and reduce the number of iterations of the algorithm; Secondly, the algorithm uses an improved inverse cotangent function to construct the sample weight of each sample point for the class and uses it to improve the membership matrix of the FCM algorithm. In this way, the algorithm improves the shortcomings of FCM algorithm to randomly obtain membership matrix, and improves the accuracy of clustering. The experimental results show that the proposed algorithm has good clustering effect, smaller number of iterations and better time performance.