Based on phase space delay-coordinate reconstruction of a chaotic dynamics system, we propose a local prediction of chaotic time series using a support vector machine (SVM) to overcome the shortcomings of traditional localprediction methods. The simulation results show that the performance of this proposed predictor for making onestep and multi-step prediction is superior to that of the traditional local linear prediction method and global SVM method. In addition, it is significant that its prediction performance is insensitive to the selection of embedding dimension and the number of nearest neighbours, so the satisfying results can be achieved even if we do not know the optimal embedding dimension and how to select the number of nearest neighbours.