Based on the vector aberration theory, an analysis method of aberration field distribution induced by Zernike polynomial freeform surface is proposed. The analysis expression of aberration by inducing freeform surfaces into the optical system with residual astigmatism and coma is deduced. The aberration nodal distribution leaded by freeform surface which is away from the stop position is simulated by optical design software. The simulation result is agreed with the analysis result which proves the method can be utilized to analyze the freeform optical system aberration. Lastly, a three mirror optical system with large field of view including freeform surface is designed by utilizing this method. The effective focal length is 850 mm, F number is 6.5, the field of view is 20°× 2°. The result shows that the system distortion is lower than 0.25％ through the field of view. The system can achieve the requirement of earth observation.