Accurately predicting inter-frame motion information plays a key role in video prediction tasks. In this paper, we propose a Motion-Aware Unit (MAU) to capture reliable inter-frame motion information by broadening the temporal receptive field of the predictive units. The MAU consists of two modules, the attention module and the fusion module. The attention module aims to learn an attention map based on the correlations between the current spatial state and the historical spatial states. Based on the learned attention map, the historical temporal states are aggregated to an augmented motion information (AMI). In this way, the predictive unit can perceive more temporal dynamics from a wider receptive field. Then, the fusion module is utilized to further aggregate the augmented motion information (AMI) and current appearance information (current spatial state) to the final predicted frame. The computation load of MAU is relatively low and the proposed unit can be easily applied to other predictive models. Moreover, an information recalling scheme is employed into the encoders and decoders to help preserve the visual details of the predictions. We evaluate the MAU on both video prediction and early action recognition tasks. Experimental results show that the MAU outperforms the state-of-the-art methods on both tasks.