Long-distance noncooperative target ranging echo point cloud acquired by single-photon LiDAR is sparse and contains a significant amount of noise, which renders it difficult to accurately extract effective echo and distance trajectory in real time. Therefore, a real-time extraction algorithm for single-photon LiDAR ranging trajectory is proposed based on its temporal and spatial correlation. First, the distance-trajectory-extraction problem is converted into a curve-recognition problem based on the Hough transform, and sparse echo point cloud data is extracted from point-cloud data containing a significant amount of noise by adaptively optimizing the Hough transform. Subsequently, the extracted echo point cloud is used as the observation value of Kalman filtering to accurately estimate the target distance trajectory. In frame segments in which the target is occluded or noise exerts a significant effect, thus resulting in frame segments with missing targets owing to occlusion or severe noise, the distance and velocity information of the target in the previous frame is utilized to predict the state of the target in the current frame. The proposed algorithm processes the simulated data with a minimum signal-to-noise ratio of -9.42 dB under extreme motion conditions. Additionally, the smallest root-mean-square error of the target's distance is 0.833 m, and the lowest leakage-detection rate is 0.05. Moreover, the algorithm offers better real-time performance and can output the target distance continuously and accurately at a frame rate of 100 Hz. During the processing of the measured data, when the echo missed 885 frames continuously, the distance trajectory predicted by the algorithm deviates from the actual value by only 0.2 m. Thus, the proposed algorithm provides an effective method for the real-time accurate extraction of single-photon LiDAR ranging trajectory.