Abstract: According to Maxwell’s equations and heat-conduction differential equation, a mathematical model is developed to describe the distribution of electromagnetic field, inductive eddy current and thermal field for multi-stage induction coilgun. Based on the finite element method(FEM) analysis of electromagnetic and thermal fields, a three-dimensional FEM model is built. When ignoring the inter-stage effect, armature temperature rise calculated in multi-stage is equivalent to multiple armature temperature rise calculated in single-stage. the practical induction heating quenching process is simulated by using ANSYS software. The relationship between the physical parameters of the coilgun and the resulting temperature is considered during the computation. The simulated results indicate that: 1.