Predicting future human motion plays a significant role in human-machine interactions for a variety of real-life applications. In this paper, we build a deep state-space model, DeepSSM, to predict future human motion. Specifically, we formulate the human motion system as the state-space model of a dynamic system and model the motion system by the state-space theory, offering a unified formulation for diverse human motion systems. Moreover, a novel deep network is designed to build this system, enabling us to utilize both the advantages of deep network and state-space model. The deep network jointly models the process of both the state-state transition and the state-observation transition of the human motion system, and multiple future poses can be generated via the state-observation transition of the model recursively. To improve the modeling ability of the system, a unique loss function, ATPL (Attention Temporal Prediction Loss), is introduced to optimize the model, encouraging the system to achieve more accurate predictions by paying increasing attention to the early time-steps. The experiments on two benchmark datasets (i.e., Human3.6M and 3DPW) confirm that our method achieves state-of-the-art performance with improved effectiveness. The code will be available if the paper is accepted.