In cellular networks, the base station power consumption is not simply proportional to the traffic loads of its coverage. As the traffic load fluctuates spatially and temporally, the base stations consequently suffer from heavy energy wastage when the traffic loads of their coverage are low. In this paper, we propose a grid-based energy saving scheme over predicted traffic loads. We firstly take advantage of the spatial-temporal pattern of traffic loads and employ the compressed sensing method to predict the future traffic loads. Then, we propose a grid-based energy saving scheme to improve the energy efficiency through turning some base stations into sleeping mode while ensuring the quality of service. Results of the simulation with real traffic loads¹ finally show the accuracy of the traffic load prediction and large energy efficiency improvement.