A novel free electron laser with multilayer film wiggler is reported, and the spontaneous radiation of the motion of an electron in the multilayer film wiggler has been discussed by using virtual photon and Compton scattering method. Antiferromagnetic coupling in ferromagnetic-nonmagnetic (such as (Fe/Cr)N) multilayers has been observed in experiments. Therefore the wiggler can be made of magnetic multilayers (MLs). Considering the space cycle of magnetostatic field is only 7.8 nm, the precise wavelength calculation and the precise radiating power calculation should consider the reaction propulsion of electron. The precise computing formulas of wavelength and radiating power are investigated, the results show that the formulas of both wavelength and radiating power include Compton wavelength.