An improved Lidar odometer based on continuous-time spline constraints is proposed to address the problem of motion trajectory drift caused by sudden turning and swaying of the laser radar owing to road bumps and other road conditions. By assuming motion discontinuity, the accuracy of point cloud matching is improved by scanning keyframes and spline segmentation, and then adding spline constraints. By using the improved iterative nearest neighbor (ICP) algorithm for frame-to-map matching, the drift of motion trajectories can be effectively suppressed. The experimental results of using the KITTI mileage and laboratory-collected mileage datasets show that the proposed Lidar odometer algorithm reduces the global average error of the motion trajectory by 12.43% and 29.40%, respectively. Compared with existing methods that are based on geometric features, the proposed Lidar odometer is stable and effectively suppresses motion trajectory drift, improving the performance of the Lidar odometer.