In order to solve the problem that the traditional K-medoids clustering algorithm needs to specify the number of clusters, which is sensitive to the initial cluster center and the slow convergence speed, the method of density peak optimization is used for solution. In this paper, we propose Fuzzy density peak K-medoids (FDP_K-mediods) algorithm. In the improved Kmedoids algorithm, the local clustering center is obtained by calculating the local density and the high density distance, and then merged into the global clustering center, which can adaptively generate the initial clustering center and determine the number of clusters. The experimental results show that our scheme can adaptively generate the initial clustering center and determine the number of clusters with some practical and artificial data sets. Compared with the traditional K-medoids algorithm, the improved algorithm can accurately obtain the number of clusters and improve the algorithm's performance.