The zoom lens theory and re-imaging theory of dual field-of-view infrared optical systems are presented. The focus length and space of each element in a lens group are solved according to the object-image exchanging rule in Gaussian imaging principle. The solving method for an initial structure of the double separate lens in a lens group is described in detail. The basic theory for solving with PW method is analyzed. Finally, an dual field-of-view infrared optical system based on a 320240 pixel cooled staring middle infrared focal plane array is designed according to the above theory. The optical system is evaluated in image quality with the optical modulation transfer function. The result shows that the design has a high image quality and can meet the requirements of practical applications.