Compared with the impulse LiDAR, the single-photon LiDAR has higher measurement sensitivity in the prominent feature, especially for space-based long-distance imaging. The distance measurement and the detection probability are the critical performance for LiDAR. The ranging of single-photon LiDAR is mainly different from the photon ranging of pulsed LiDAR. Dead time has a significant effect on distance measurement accuracy and detection probability, which are key parameters for detectors when implementing sound control. Therefore, the model of detector dead time, measurement accuracy, and detection probability should be established, and simulation results that meet application requirements should be achieved. Based on the single-photon ranging theory, the dead time, measurement accuracy, and detection probability model of single-photon LiDAR are studied. Furthermore, the systematic simulation of different contrasts is carried out according to the model. The simulation results demonstrate that the model can accurately perform the relationship between dead time and single-photon LiDAR system parameters. The research results can prove the design and verification of single-photon LiDAR dead time.