In this paper, local support vector machine (LSVM)， which combins the advantage of traditional local prediction methods and support vector machines， is proposed to make local predictions of spatiotemporal time series. The LSVM is also used to discuss the selection of embedding dimension and the number of nearest neighbours, the coupling-way and the coupling coefficients of spatiotemporal chaotic systems that influence on the local predictions of spatiotemporal chaotic time series. Experimental results show that the LSVM can not only make better predictions of spatiotemporal chaotic time series than that of local zero-order methods and local linear methods and global support vector machine, but the computational complexity can also be reduced greatly compared to the global support vector machine. Moreover, the LSVM is insensitive to the selection of embedding dimension and the number of nearest neighbours. In addition, the local prediction performance of spatiotemporal chaotic time series is influenced by the coupling-way and the coupling coefficients of spatiotemporal chaotic systems.