The geometric aberration of centered refracting double-plane symmetric optical systems (DPSOS) is investigated. For DPSOS with different defocus values in the tangential plane and the sagittal plane (astigmatic wavefront), a pair of curved reference surfaces which vanishes the quadratic terms of the optical path difference (OPD) between a general ray and a reference ray are deduced. With the curved reference surfaces, the primary (fourth-order) wave aberration function for DPSOS is calculated and analyzed, which can be used for beam shaping designs with astigmatic input wavefront, such as slab lasers and semiconductor lasers. Further, the proposed curved reference surfaces can be applied to analyze the aberrations of general DPSOS.