Induction heating is a process that is accompanied with magnetic and thermal situation. This paper presents a simulation of a magneto-thermal coupled problem of an induction heating process for moving inductor coil. In the magnetic and thermal analyses, temperature-dependent magnetic and thermal material properties were considered. As the inductor coil moves in the process, solution domains corresponding to inductor changes into those of the air, and the solution domains of air change into those of the inductor. For these reasons, modeling of induction heating process is very difficult with general purpose commercial programs. In this paper, induction heating process for moving coil was simulated with the concept of traveling the position of the heating planes. Finite element program was developed and finite element results were compared with the experimental results.