Based on the nodal aberration theory, an aberration analysis method for pupil off-axis freeform surface optical system with Zernike polynomial is proposed. The analytical expressions of third-order astigmatism and coma of the pupil off-axis freeform surface system are deduced. The impact of freeform surface on the distribution of aberration nodes of pupil off-axis system is analyzed. According to the aberration distribution properties, with pointed optimization of the Zernike terms, a pupil off-axis freeform surface space telescope optical system is designed. The effective focal length is 25 m, the pupil diameter is 2 m and the field of view is 1.2°×1.2°. By introducing the freeform surfaces, the third-order astigmatism and coma nodes are both moved back to the field of view. Therefore, the asymmetric aberrations induced by pupil off-axis are balanced, the point spread functions (PSF) ellipticity are controlled effectively, and the measurement errors of star observation are decreased. The final imaging quality is closed to the diffraction limit, which meets the requirements.