Abstract: A set of coupled nonlinear threedimension differential equations for the FEM amplifier with elliptical waveguide and planar wiggler is derived. Based on these equations, a universal numerical simulation program is developed independently. The characteristics of this FEM including the evolution of power, saturation efficiency and bandwidth are investigated using the numerical method. Electron momentum spread ,spacecharge and wiggler taper are also considered. Electron beam is modeled to adiabatically inject by allowing the wiggler amplitude to increase from zero to a constant amplitude and the spacecharge is analyzed in terms of GT mode expansion method. The results show that saturated output power is 360kW, efficiency is up to 9.2% using wiggler taper and 3dB bandwidth is 6.9% of