This paper presents a paraxial lens design method for anamorphic zoom lenses with double telecentricity. Four types of such lens systems are provided, which are the Y-X-Y-Y type, the Y-Y-Y-X type, the Y-X-Y-X type, and the Y-X-X-Y type. For each lens type, it can work in two different conditions: (a) the distance between the object and the image is fixed during anamorphic zooming, or (b) the magnifications in the tangential plane and the sagittal plane can be changed independently by changing the interval lens distances. For each condition, given the optical power of each lens component and the design parameters, such as the total length, the magnifications in the tangential plane and the sagittal plane, and the anamorphic ratio, formulas determining the interval distances between lens components, the object position, and the stop position are provided. Eight examples of double-telecentric anamorphic zoom lenses are provided, and all the examples are tested in Zemax, which shows the validity of the proposed design method.