Recently, a new clustering method called maximum margin clustering (MMC) was proposed. It extended the support vector machine (SVM) thoughts to unsupervised scenarios and had shown promising performances. Traditionally, it was formulated as a non-convex integer optimization problem which was difficult to solve. In order to alleviate the computational burden, the efficient cutting-plane MMC (CPMMC) [wang2010mmc] was proposed which solved the MMC problem in its primal. However, the CPMMC is restricted to linear kernel. In this paper, we extend the CPMMC algorithm to the nonlinear kernel scenarios, which is the proposed sparse kernel MMC (SKMMC). Specifically, we propose to solve an adaptive threshold version of CPMMC in its dual and alleviate its computational complexity by employing the cutting plane subspace pursuit (CPSP) algorithm [joachims2009sparse]. Eventually, the SKMMC algorithm could work with nonlinear kernels at a linear computational complexity and a linear storage complexity. Our experimental results on several real-world data sets show that the SKMMC has higher accuracies than existing MMC methods, and takes less time and storage demands than existing kernel MMC methods.