A high zoom ratio optical system with f=10 mm~500 mm was designed. The initial structure and reasonable Gauss solution were given by Gauss optical computing based on positive mechanical compensation principle. Two novel aspheric surfaces were introduced in this system, which could provide more degrees of freedom for optical design, correct aberration in optical systems effectively, as well as the complexity of system, and this is advantageous for achieving high zoom ratio system. The second order spectrum from telephoto was corrected by a group of double-layer harmonic diffractive element, that could reduce the number of sheets of lens and make the system more compact. The curves of zoom group and the compensating group were simulated, and the modulation transfer function(MTF) curve was analyzed in the case of 10mm to 500mm focal length. From the above we can see that, the system can satisfy the change regulation of the mechanical compensation cam curve, the curve is smooth, and a smooth zoom is achieved. When Nyquist frequency is 50 lp/mm, the MTF is greater than 0.6, and high quality image is achieved.