Abstract: The Gaussian optics is traditionally used to calculate the focus of every element and the distances between them in a zoom system. This design method is different from the traditional one. All the parameters of the zoom system are achieved with mathematic software, which solves a nonlinear equation group set up with a ray-transmission matrix of the zoom lens, based on the theory of the matrix optics. At last, the application of matrix optics is demonstrated in designing a zoom system of a general camera lens.