Human motion prediction aims to forecast an upcoming pose sequence given a past human motion trajectory. To address the problem, in this work we propose FreqMRN, a human motion prediction framework that takes into account both the kinematic structure of the human body and the temporal smoothness nature of motion. Specifically, FreqMRN first generates a fixed-size motion history summary using a motion attention module, which helps avoid inaccurate motion predictions due to excessively long motion inputs. Then, supervised by the proposed spatial-temporal-aware, velocity-aware and global-smoothness-aware losses, FreqMRN iteratively refines the predicted motion though the proposed motion refinement module, which converts motion representations back and forth between pose space and frequency space. We evaluate FreqMRN on several standard benchmark datasets, including Human3.6M, AMASS and 3DPW. Experimental results demonstrate that FreqMRN outperforms previous methods by large margins for both short-term and long-term predictions, while demonstrating superior robustness.