A surface discharge non-equilibrium plasma model of air-polyimide under pulsed electrical stress is established, by considering the reaction of charged particles on the dielectric surface and the secondary electron emission caused by the condition that high-energy particles bombard the material surface. The model defines the chemical reaction of air discharge by using simplified set of reactions, which greatly reduces the complexity of the model. To avoid the negative value of particle density in the process of solution, the logarithmic finite-element method is used to solve the model established, so as to implement the dynamic simulation of the surface discharge process. Also, the temporal and spatial evolution of the microparameters such as charge and electric field distribution during discharge are obtained, and the reliability of the model is verified by experiments in terms of discharge development pattern and surface charge accumulation. By comparing the development process of surface discharge under single pulse and repetitive pulses, it can be seen that surface discharge develops from needle electrode to ground electrode under both repetitive pulses and single pulse stress, but the relationship between the discharge propagation time under repetitive pulses and pulse repetition rate is a 'u' curve, and the inflection point moves to higher repetition rate region with the increase of voltage.