Due to the disadvantages such as sensitive to the initial selection of the center, slow convergent speed and poor accuracy in traditional K-medoids clustering algorithm, a novel K-medoids algorithm based on improved Granular Computing (GrC), granule iterative search strategy and a new fitness function was proposed in this paper. The algorithm selected K granules using the granular computing thinking in the high-density area which were far apart, selected its center point as the K initial cluster centers, and updated K center points in candidate granules to reduce the number of iterations. What's more, a new fitness function was presented based on between-class distance and within-class distance to improve clustering accuracy. Tested on a number of standard data sets in UCI, the experimental results show that this new algorithm reuduces the number of iterations effectively and improves the accuracy of clustering.