To solve the problem of testing the sensitivity under electromagnetic pulse radiation for a hot bridge wire electro-explosive device (EED), this paper simulated and analyzed the correlation between the critical ignition current under steady and pulse excitation. The simulation results showed that, under single pulse excitation, the critical ignition current of the EED decreases with the increase in the pulse width, and the variation law can be divided into three pieces: adiabatic, transition, and constant; while under pulse train excitation, due to the thermal cumulative effect, the critical ignition current is related to both material properties and excitation parameters. By analyzing the simulation results and considering the thermal ignition theory, the mathematical model of the critical ignition current under pulse excitation was established, and the mathematical model showed that under pulse train excitation, the critical ignition current is relevant not only to the single pulse excitation critical ignition current, pulse period, and duty cycle, but also to the ratio of single pulse and steady excitation critical ignition current and the thermal time constant. It was verified that the errors between the theoretical values obtained from the mathematical model and the results obtained from the simulation were within 2.5%.