High voltage pulse discharge technology has been proven to have good prospects in rock fragmentation and drilling, yet its mechanisms are not fully understood and there are many influencing factors, which are the main obstacles to restricting the commercialization of this method. This study investigates the discharge channel responses in the process of high voltage pulse discharge crushing granite by using physical-mathematical model and numerical simulation model, which includes the state, electrical characteristics and physical feature of the discharge channel, and analyzes the effect of the initial generator capacitor voltage. The results show the discharge voltage and current, the maximum depth and width of the discharge channel developing into the granite obtained based on the simulation can effectively reflect the experimental results. In addition, the simulation of the initial generator capacitor voltage from 240kV to 420kV illustrates the number, time, cross-sectional area of the main discharge channel between the two discharge electrodes, power and energy of injection into discharge channel, the maximum conductivity, length, pressure, radius of the discharge channel and the extended maximum depth of the main discharge channel increase as the initial generator capacitor voltage increases. This suggests that to enlarge the initial voltage of the high voltage pulse discharge power supply can improve the fragmentation effect. This study has a certain guiding significance for improving crushing efficiency, optimization of the discharge electrode structure and selection of the power supply parameters in the process of high voltage pulse discharge crushing granite.