This paper presents a new online clustering algorithm called SAKM (Self-Adaptive Kernel Machine) which is developed to learn continuously evolving clusters from non-stationary data. Based on SVM and kernel methods, the SAKM algorithm uses a fast adaptive learning procedure to take into account variations over time. Dedicated to online clustering in a multi-class environment, the algorithm designs an unsupervised neural architecture with self-adaptive abilities. Based on a specific kernel-induced similarity measure, the SAKM learning procedures consist of four main stages: Creation, Adaptation, Fusion and Elimination. In addition to these properties, the SAKM algorithm is attractive to be computationally efficient in online learning of real-drifting targets. After a theoretical study of the error convergence bound of the SAKM local learning, a comparison with NORMA and ALMA algorithms is made. In the end, some experiments conducted on simulation data, UCI benchmarks and real data are given to illustrate the capacities of the SAKM algorithm for online clustering in non-stationary and multi-class environment.