Pulsed power technology is one of the technological foundations in high and new technology research, which has extremely broad development and application prospect. Gas switch is one of the key elements in pulsed power devices, and electrode erosion is a key restrictive factor in high-power gas switch development and application. According to the 1-D equation of heat conduction and thermal equilibrium equation near the electrode surface, this paper researches the electrode heat conduction mechanism, establishes the electrode erosion calculation model, calculates electrode erosion heat fluxes and their peak powers caused under different discharge conditions, and proceeds to calculate the depth of electrode etch pit. Calculation results indicate that arc joule heat is the main reason for electrode erosion when discharge current is not too high. In the light of different discharge parameters, that is, peak current, electric quantity, and current waveform, as well as single discharge electrode erosion experiments, the calculation formula of etch pit depth is fitted. The results indicate that model and fitted calculation results are relatively approximate to the experiment results.