For modern multimedia devices, such as digital photo and video cameras, compact size of optical system is becoming more and more important. This work is dedicated to zoom lens design and second-order derivative optimization method of designed system with using of computer program which allows to design a small-size high-quality system. For lens designing we are using the third order aberration theory and an equation set describing interrelations of system parameters, such as minimum length of system, focal length of each component, their shifts and distances between them. Also equations include conditions of uninterrupted focusing on CCD. Zoom lens consists of three components, two of which are movable. First component is immovable. Number of lenses in each component (two or three) is determined automatically in according to conditions of minimum aberrations and manufacturability. Designed system contains only second-order surfaces with eccentricities. Complete correcting of aberrations consists of two phases. First, the best constructive parameters (radii of curvature, thicknesses and eccentricities) are determined for designed system. The second-order derivative method is used for that. The main feature of this method is the using of Hesse matrix of wave aberration function. Second, for selected surfaces aspherical coefficients are determined. Wave aberration's dependence of constructive parameters and aspherical coefficients is used.