Forecasting the motion of surrounding dynamic obstacles (vehicles, bicycles, pedestrians and etc.) benefits the on-road motion planning for autonomous vehicles. Complex traffic scenes yield great challenges in modeling the traffic patterns of surrounding dynamic obstacles. In this paper, we propose a multi-layer architecture Interaction-aware Kalman Neural Networks (IaKNN) which involves an interaction layer for resolving high-dimensional traffic environmental observations as interaction-aware accelerations, a motion layer for transforming the accelerations to interaction-aware trajectories, and a filter layer for estimating future trajectories with a Kalman filter. Experiments on the NGSIM dataset demonstrate that IaKNN outperforms the state-of-the-art methods in terms of effectiveness for trajectory prediction.