In the process of continuous zoom optical system design, the aberration automatic design demands prior experience , complicated algorithm and massive calculation. In order to overcome these difficulties, the method of using subtractive linear equations to carry out the aberration automatic design is proposed. With this method, a continuous zoom optical system of visible spectrum is designed. Using Gaussian optics to calculate the paraxial structural parameters of the system; the application of subtractive linear equations in the aberration automatic design make the value of primary aberration coefficients SI , SII and SIII approximately equal at different focal lengths positions; based on the results of the aberration automatic design, the initial structural parameters of system are calculated; the aberrations are corrected by Zemax optical design software. The design result indicates that the focal length could vary from 20 mm to 300 mm continuously for this system and the modulation transfer function is always bigger than 0.4 at the spatial frequency of 50 lp/mm and every focal length position. In conclusion, the method of subtractive linear equations in the aberration automatic design can simplify the calculation, reduce the degree of relying on the prior experience and achieve high quality of image.