Long-range detection using single-photon lidar can increase the farthest detection distance, and due to the complexity of its transmission link, a mathematical model of signal-to-noise ratio for single-photon laser active detection was established. Firstly, the echo signal model of the pulsed laser in the full link of active detection considering diffraction was established, and the size of the number of signal photons received by the single-photon detector was calculated. Then, the composition of noisy photoelectrons in the active detection process was analyzed, and the number of noisy photoelectrons was quantitatively calculated. Based on the above model, the echo signal-to-noise ratio model under the consideration of the aiming deviation of the optic axis was established. A set of system parameters of a single-photon laser detection system used for theoretical model validation was simulated and analyzed, and the relationship between the laser pulse energy and the size of the echo signal-to-noise ratio was analyzed under the influence of different target detection distances and different aperture sizes of the receiving system. The results were compared with those calculated by the echo signal-to-noise ratio model based on the lidar equation, which proved the simplicity and feasibility of the mathematical model.