The optical element of free-form surface can be expressed by the fringe Zernike polynomial and the terms of initial spherical sag, coma and astigmatism are transformed into the vector forms. Based on the vector wave aberration theory, the free-form optical element characteristic of optical system initial aberration correction is analyzed. Through the analysis, the free-form surfaces in optical system have different aberration emendation specialties at different positions. The free-form optical element can be corrected in full field of view for constant initial aberration as a stop aperture (entrance pupil or exit pupil) in optical system. When the free-form surface is far from the stop aperture of optical system, due to the scaling and offset of the imaging beam aperture for an off-axis field point, the free-form surface can correcte the asymmetric initial aberration, and the relationship of different initial aberration and field of view is different.