This paper presents the procedures for an initial design containing the first and third order aberrations of a four-group, rear focus video camera zoom lens using lens modules, and the real lens design from an initial design. Lens modules in the zoom system can explicitly describe the first and third order properties of each group without detailed design. The optimum initial design with a zoom ratio of about 10X and a focal length range of 6 to 60 mm is derived by assigning appropriate first and third order aberrations to each module along with the specific constraints required for optimization. For a real lens design of each group, we set up the simultaneous equations for the first and third order aberrations, and the solutions result in the optical systems which satisfy the properties of original lens modules. As a result, the design of a zoom system using lens modules is broken down into the simple problem of designing the individual groups to satisfy sets of the first and third order properties, and quickly provides the optimum system.