As drone technology advances, using unmanned aerial vehicles for aerial surveys has become the dominant trend in modern low-altitude remote sensing. The surge in aerial video data necessitates accurate prediction for future scenarios and motion states of the interested target, particularly in applications like traffic management and disaster response. Existing video prediction methods focus solely on predicting future scenes (video frames), suffering from the neglect of explicitly modeling target's motion states, which is crucial for aerial video interpretation. To address this issue, we introduce a novel task called Target-Aware Aerial Video Prediction, aiming to simultaneously predict future scenes and motion states of the target. Further, we design a model specifically for this task, named TAFormer, which provides a unified modeling approach for both video and target motion states. Specifically, we introduce Spatiotemporal Attention (STA), which decouples the learning of video dynamics into spatial static attention and temporal dynamic attention, effectively modeling the scene appearance and motion. Additionally, we design an Information Sharing Mechanism (ISM), which elegantly unifies the modeling of video and target motion by facilitating information interaction through two sets of messenger tokens. Moreover, to alleviate the difficulty of distinguishing targets in blurry predictions, we introduce Target-Sensitive Gaussian Loss (TSGL), enhancing the model's sensitivity to both target's position and content. Extensive experiments on UAV123VP and VisDroneVP (derived from single-object tracking datasets) demonstrate the exceptional performance of TAFormer in target-aware video prediction, showcasing its adaptability to the additional requirements of aerial video interpretation for target awareness.