The clustering algorithm represented by K-means is widely used in many fields, but K-means cannot directly deal with incomplete data. k_m-means is a clustering algorithm for processing incomplete data. It reduces the impact of incomplete data on the clustering process by adjusting the calculation method of partial distance. However, the centroids selected in the initialization stage of k_m-means are unreliable, resulting in local optimal solutions. For incomplete data, a clustering algorithm that combined credibility was proposed to solve this problem. The calculation of distance was adjusted by credibility to increase the reliability of cluster centroids in the initialization stage, improving the performance of clustering algorithm. Finally, the algorithm was verified by the experimental results from the UCI and UCR dataset.