: In this paper, the thermodynamic model of single-stage and two-stage compression air source heat pump is established by distributed parameter method, and the PID control algorithm is applied to the model calculation to form a system-wide cyclic distribution parameter model based on PID control algorithm. The established model is run in a C++ environment and the experimental data is used to verify the accuracy of the model. The comparison between the experimental data and the model simulation results shows that the model makes full use of the advantages of the distributed parameter method and the PID control algorithm. Compared with the model established by the traditional lumped parameter method, the model has higher calculation accuracy . The average relative error between the simulated cop and the experimental data of the model of the two-stage compression air source heat pump is 4.91%. After adding the PID control algorithm, the operation speed of the model is improved, and the cycle of the two-stage compressed air source heat pump model is iterated five times.