A systematic approach for the aberration design of a four-component double-sided telecentric zoom lens system is presented. The Gaussian structure of the zoom system is specified previously which means the powers and movements of components are known. Each component is treated as a lens module during the design stage with specified first-order properties and third-order aberration targets. The third-order aberration targets of the first component are determined by minimizing the whole aberrations of the zoom lens system using a genetic algorithm (GA). And the aberration targets of components behind are determined by reoptimization with already fixed structures of previous components. Mean pupil spherical aberration of every component in every zoom position is adopted in the objective function to control high-order aberrations. The thin lens structure of each component can be determined from their first-order properties and aberration targets. After lens thickening and reoptimization, the zoom lens system can finally be determined.