According to the theory of H_∞ filter,an approach of small target motion prediction and tracking in infrared images was presented based on H_∞filter technology.In order to reduce the rank of the model for speeding up the velocity of image process,the filter process was analysed along horizontal orientation and vertical orientation,that is,the filter was decomposed into two filters along x and y orientation.H_∞filter is a filter technology based on the optimization of worst condition which doesn't require too much about the noise sources and it can be applied to target motion prediction and tracking in complex and clutter background.The experiments demonstrate that H_∞ filter is more exact for IR small target motion prediction and resistible to the disturbance than Kalman filter in the system which has the uncertain or unknown noise sources.