The use of the electromagnetic pump that drives sodium by the electromagnetic force is expected in the FBR system. However, a large size pumps is not put to practical use because of magnetohydrodynamical instability. In This study, the coupled FEM of electromagnetic field and incompressible fluid by using Magnetic vector potential FEM and GSMAC-FEM is proposed, and the system of electromagnetic pump is calculated by this scheme. Instability characteristics with large size pump are considered from the electromotive force by the motion and Lorentz force.