Silicon photomultiplier （SiPM）is a silicon array structure based on the Geiger mode avalanche photodiode. It not only has extremely high photon counting sensitivity and response speed， but also has the characteristics of high dynamic range and linear response under the multi-photon condition， which makes it have unique advantages in the application of photon counting LIDAR. However， due to the multi-pixel， single-time channel working mode of SiPM， its output voltage has a greater probability of pulse pile up compared with other single-photon detectors. Therefore， the detection process of SiPM under different discrimination thresholds is more complicated. To solve this problem， a SiPM photon event response model is established in this paper. Based on this， the time-domain distributions of the shielding effect and the triggering effect caused by pulse pile up are discussed. Finally， the semi-analytic detection probability and false alarm probability models of SiPM are established. At the same time， a photon counting Lidar system based on SiPM detector is built， and the theoretical model is verified by observing that the measured output voltage waveform and point cloud distribution are consistent with the theoretical model （R²>0.95）. Furthermore， the distribution of SiPM photon point cloud with different discrimination thresholds is quantitatively evaluated by the recall and precision ratio， and the optimal discrimination threshold interval is given， which has important guiding significance for the design and theoretical analysis of photon counting Lidar system based on SiPM.