To address the modeling problem for strongly spatiotemporal nonlinear dynamics and obtain an effective control performance, a data driven spatiotemporal MPC strategy is developed for nonlinear DPSs. First, a low-order spatiotemporal model is proposed based on KPCA and LS-SVM to represent the spatiotemporal nonlinear dynamics. The KPCA is used to handle the nonlinear spatial features based on kernel technique, and LS-SVM is applied for the modeling of time coefficients. Then, a spatiotemporal MPC is designed by reconstructing a new objective function with consideration of errors on not only time but also space, which overcomes the shortcoming of the traditional MPC due to fully consideration of nonlinear spatial dynamics. Finally, the spatiotemporal control strategy is verified by mathematical stability analysis and actual experiment.