Support-based clustering using kernels suffers from serious computational limitations inherent in many kernel methods when applied to very large-scale problems despite its ability to identify clusters with complex shapes. In this paper, we propose a novel clustering algorithm called Voronoi cell-based clustering to expedite support-based clustering using kernels. In contrast to previous studies, including the basin cell-based method, the proposed method achieves computational efficiency in both the training phase to construct a support estimate using sampled data to reduce the evaluation of kernels and the labeling phase to assign a cluster label on each data point nearest its representative point. The performance superiority of the proposed method over the other basin cell-based methods in terms of computational time and storage efficiency is verified by various experiments using benchmark sets and in real applications to image segmentation.