In order to study the breakdown process of the insulating medium of the needle-needle electrode under the action of high-voltage pulse discharge, the HV-LAB simulation software was used to study the discharge channel formed in the three kinds of insulating media, namely water, transformer oil, and air, and the three-dimensional model of the discharge breakdown insulating medium was designed. The process of discharge channel expansion, voltage, current, power, and energy loss in the discharge channel is analyzed. The results show that in the process of high-voltage pulse discharge breakdown of the insulating medium, the formation time of the discharge channel of transformer oil is long, the energy is accumulated, the number of discharge channels is less, the horizontal isopotential lines are dense, and the energy is concentrated. Under the same discharge conditions, the energy consumption of transformer oil in the process of high-voltage pulse discharge is the least. The results of this study can provide a reference for the selection of high-voltage crushing insulation medium.