Kernel approaches can improve the performance of conventional clustering or classification algorithms for complex distributed data. This is achieved by using a kernel function, which is defined as the inner product of two values obtained by a transformation function. In doing so, this allows algorithms to operate in a higher dimensional space (i.e., more degrees of freedom for data to be meaningfully partitioned) without having to compute the transformation. As a result, the fuzzy kernel C-means (FKCM) algorithm, which uses a distance measure between patterns and cluster prototypes based on a kernel function, can obtain more desirable clustering results than fuzzy C-means (FCM) for not only spherical data but also nonspherical data. However, it can still be sensitive to noise as in the FCM algorithm. In this paper, to improve the drawback of FKCM, we propose a kernel possibilistic C-means (KPCM) algorithm that applies the kernel approach to the possibilistic C-means (PCM) algorithm. The method includes a variance updating method for Gaussian kernels for each clustering iteration. Several experimental results show that the proposed algorithm can outperform other algorithms for general data with additive noise.