An anamorphic magnification extreme ultraviolet (EUV) lithographic objective could increase the size of the exposure field at a wafer in the orthogonal scanning direction to improve the throughput of the lithographic system. In this paper, we present a curvatures combination method for an anamorphic magnification EUV lithographic objective with high numerical aperture (NA). This method achieves an anamorphic magnification initial structure by use of the double-curvature surfaces, which are formed by combining the curvatures of the corresponding surfaces into two coaxial spherical systems. A series of control measures is taken to design the two coaxial spherical systems for ensuring the rationalities of the initial structure and the surfaces after combining. The image quality of the anamorphic initial structure is optimized by a gradual optimization process. Finally, as an example, we design an Mx1/4 and My1/8 anamorphic magnification EUV lithographic objective with the presented design method. This objective achieves 0.5 NA and a 26 mm×16.5 mm exposure field at the wafer. The wavefront error RMS reaches 0.06λ (λ=13.5 nm), and the distortion is less than 2.8 nm. The design result proves the availability of the curvatures combination method.