A nonlinear analysis is presented for a free-electron laser with an electromagnetic pump in the presence of a guide magnetic field bu using kinetic theory based on the Vlasov-Maxwell equations. Linear and nonlinear dispersion relations are derived. The nonlinear growth rates of the free-electron laser are obtained for the weak and strong pump limits. Then according to the electron trapping mechanism the energy conversion efficiency is calculated. The results show that the guide magnetic field may lead to substantial enhancements in the growth raises and efficiency as long as reasonable parameters are chosen.