This paper presents the application of least squares support vector machines (LS-SVMs) to design of an adaptive damping controller for superconducting magnetic energy storage (SMES). To accelerate LS-SVMs training and testing, a large amount of training data set of a multi-machine power system is reduced by the measurement of similarity among samples. In addition, the redundant data in the training set can be significantly discarded. The LS-SVM for SMES controllers are trained using the optimal LS-SVM parameters optimized by a particle swarm optimization and the reduced data. The LS-SVM control signals can be adapted by various operating conditions and different disturbances. Simulation results in a two-area four-machine power system demonstrate that the proposed LS-SVM for SMES controller is robust to various disturbances under a wide range of operating conditions in comparison to the conventional SMES.