The development of extreme ultraviolet(EUV) lithographic objective design is toward the direction of an anamorphic magnification objective system, and large field of view and high numerical aperture (NA) for projection objectives are both needed, which cause an extreme increase of incident angle and incident angle range of an objective lens system, so new methods for multilayer film design of anamorphic magnification EUV lithography objective systems are needed to explore. A progressive optimization multilayer film design method is presented to increase the reflectivity but not to change the imaging performance. This method is successfully applied to design the multilayer films of an anamorphic magnification EUV lithography objective system with NA=0.6. The results show that the average reflectivity of each mirror is higher than 65% and the reflectivity peak-to-valley value of each mirror is less than 3.35%, meanwhile, a good uniformity of reflectivity is maintained.