The optical zoom of three-mirror non-coaxial system is reached by introducing two deformable mirrors. The matrix optics is employed to analyze the first order characteristic of optical system and obtain system focusing formula. Combining the features of non-coaxial zoom system and aberration theories of plane-symmetric optical system, the conditions of removing the spherical aberration, the constant astigmatism, the constant coma are deduced. Meanwhile, the arched distortion produced by tilt image is eliminated according the Scheimpflug condition. Finally, a new design of all-reflection non-coaxial zoom objective is presented. The results indicate that maximum root-mean-square radius is from 5.4791 μm to 11.117 μm, which satisfies the zoom objective lens specification. The design principles and methods provide a good quest for further making use of deformable mirror to design zoom system.