Abstract: During the active space experiments of radiating the modulated electron beam, the linear and nonlinear interaction between the electron beam and background plasma may excite whistler wave. Characteristics of the excitation are determined by many factors, including velocity, relaxation characters of electron beam, the frequency of excited waves, and the density of background plasma. The relaxation characteristic length of the modulated electron beam is one of the important factors. In this paper, the influence caused by the exponential attenuation relaxation characteristic length of the modulated electron beam upon the characteristics of the wave excited by the electron beam were studied. Through solving the wave equation when the electron beam is injected into the homogeneous anisotropy space plasma, the solution of the dispersion equation and the Poynting vector representation of the excited wave are obtained. It was shown that the wave radiation intensity excited by the modulated electron beam is enhanced efficiently when the relaxation characteristic length of the electron beam is comparable with the characteristic size of inhomogeneous background plasma.