Lidar motion compensation is a crucial step in detection of dynamic background targets in smart cars. Herein,a motion compensation algorithm is proposed based on lidar. Firstly, the pose change matrix of the vehicle body between the previous and the current scan periods is solved using quaternion method. Secondly, according to the characteristics of the static scene and the data packets generated by the historical lidar data frame, the Gaussian mixture model is used to model the background over time coordinate system. The Gaussian mixture model is prone to failure in dynamic scenes, therefore, in this study, the dynamic background is first converted into a static background by motion compensation. Then, the Gaussian mixture model is used to deal with all historical frames in the time list, and feature points of the original point of the moving target are found at T moment. The alignment of feature points with the points in the current frame is used to further refine the new position of matching points in the current frame. Experimental results show that the proposed method can successfully estimate and compensate for the background motion and is suitable for real-time detection of moving targets in 3D environments.