A multi-step trajectory prediction method based on group sparse coding Kalman filtering for mobile target is proposed in this paper. Firstly, a group sparse coding is introduced, and just at that time, a simple multi-step linear prediction model is obtained by one learning, overcoming the problem that prediction accuracy is low due to the inadequate historical data with the traditional method. And then, the minimum angle regression algorithm is utilized for calculating the sparse coefficients of the above model to further improve the estimation accuracy of the model coefficients. The basic Kalman filtering algorithm is modified in combination with the group sparse coding method to ensure the precision in the prediction output. Finally, the effectiveness of the presented approach is verified by the simulation comparison among the traditional BP network, long short time memory network and the group sparse coding method.