Based on the third-order aberration theory,the problem that off-axis aberrations in the main types Galilean and Keplerian beam expanders can't be corrected is worked out. With reasonable analysis of optical path,a new type beam expander with wide aperture and bigger field angle and large relative aperture in which the on-axis and off-axis aberration are both perfectly corrected is designed. It has much better optical performance than the two classical types. An example is presented. The clear entrance of its objective is 300 mm and focal length is 800 mm,its magnitude ratio is 30 and the primary working wavelength is 0.6328 μm. The results of optical design have been given. When the distances among the lenses of eyepiece and the distance between the objective and eyepiece are adjusted reasonably,the beam expander can be used in three wavelengths.