Abstract: We made a brief summary of the development and application of free-form surface, introduced the research status of free-form surface in space optical system abroad, described the characteristics of three kinds of free surface mathematical models and the aberration balancing ability, focused on the aberration characteristics of free-form surface optical system compared with the axisymmetric system and plane-symmetric system. In addition, we presented the aberration controlling and evaluation method of the free-form space optical system. Finally, we gave the design results of the freeform surface multi-spectral camera adopting Zernike polynomial representations. The results show that the imaging field of view is 76, it adopts telecentric optical path design ; the wide field of view MTF is superior to 0.56, and it is applicable for space multispectral imaging.