A new circuit model for using the avalanche photodiodes to detect infrared single photon is proposed, which combines the requirements of a single photon detector control circuit and features of the electric pulses generator by transient process of transmission lines. The simulation results are given for the new circuit model and the emphasis is laid on the analysis of the feasibility of the circuit model in using the gate mode scheme of the avalanche photodiodes to detect infrared single photon and the influence of each electrical component on the performance of the circuit model. Finally, optimal parameters of the electrical components and the gate-mode with the quenching circuit model are demonstrated.