With the development of various disciplines, most of the traditional clustering algorithms for numerical data cannot adapt to more complex datasets. The introduction of granular clustering breaks through the bottleneck of this research field. Previous studies mainly focus on interval, triangular and trapezoidal granular data to carry out granular clustering. However, for Gaussian granularity, there is little involvement. Aiming at such problem, in this study, we propose the Kernel Cutset-type Possibility C-Means (KC-PCM) algorithm of granular clustering for Gaussian granularity. Firstly, a new granularity weight is designed for each Gaussian granularity with normalized granularity quality based upon the principle of justifiable granularity. Secondly, the Gaussian kernel distance is employed instead of Euclidean distance to measure the distance between granular data. Thirdly, the KC-PCM algorithm is proposed based on the granularity weight and the Gaussian kernel distance. Lastly, we evaluate and compare the performance of some related granular clustering algorithms on artificial and UCI datasets. It is validated that the KC-PCM algorithm can effectively solve the overlapping problem of cluster centers in the PCM algorithm series. By contrast with the related granular clustering algorithm, the cluster center obtained by KC-PCM is closer to the actual cluster center, and the obtained reconstruction error is smaller, and the polygonal convergence trend of KC-PCM is more significant. As a consequence, the performance of KC-PCM is superior over other algorithms.