Zoom lens is widely used, it can achieve both wide field of view to observe and narrow field of view to get high resolution image. Alvarez lens (AL) is used in zoom lens to achieve continuous change of focal length in a large range through small lateral movements. However, AL has asymmetric aberrations and the aberrations are difficult to be compensated by other lenses. Firstly, in order to correct on-axial aberrations, the relationship between aberrations in AL and the coefficients of free-form surfaces is analyzed by using wave aberration theory, the factors that affect the decentration of the symmetry center of aberration field is also analyzed. Secondly, a five-group zoom lens is proposed based on the aberration characteristics in AL and the principle of minimizing lateral movement. Finally, using the above theory, a medium-wave infrared continuous zoom lens is designed. The zoom lens has good imaging quality and small lateral movements, verifying the correctness of the above theory.Fringe Zernike polynomial wave aberration is used in present study to analysis the aberration in AL. Firstly, the relationship between the wave aberrations of each order on-axis and the lateral movement, spacing, and aperture of AL are analyzed. According to thin-element approximation of AL, its surface needs to extend to higher-order polynomials, and the relationship between the coefficients of free-form surfaces and the Fringe Zernike wave aberration coefficient is given. Secondly, the relationship between off-axis aberrations, lateral movement, spacing, and aperture of AL are analyzed, and their effects on the decentration of aberrations field center are given. Finally, according to the aberration of AL and the principle of minimizing movement, a five-component zoom lens is proposed. The zoom equation is given with Gaussian Brackets, and a design example is provided.Through theoretical calculations and simulations, it is found that aperture, lateral movement, and spacing are the main factors affecting the aberration of AL. When the focal length is fixed, the aberration of AL on-axis and the decentration of the AL aberration field center is smaller with smaller aperture, larger lateral movement, and smaller spacing. The decentration of the AL aberration field center is related to the asymmetric air gap of the AL. The larger lateral movement is, the smaller the polynomial coefficient is, and the less asymmetric it is. At the same time, reducing the spacing can also minimize the impact of asymmetry. Most importantly, the asymmetric aberration of AL on-axis such as primary and secondary coma, trefoil and tetrafoil can’t be corrected by other lenses. These aberrations will be directly added to the optical system, so they must be corrected by AL itself. With the lager aperture and smaller lateral movement, the value and order of aberration will be larger and higher, so it is necessary to extend the free-form to higher order xy polynomials. In most cases, the aberrations on-axis can be corrected effectively by increasing the order of polynomial to seventh order. At this point, the center of coma moves to the central field of view, meanwhile, astigmatism and field curvature decreases slightly, with no significant change in the symmetry center. The designed five-element zoom lens places two pairs of AL in the middle of three groups, with the front-fixed group and the middle-fixed group reducing the AL aperture in order to reduce the aberrations of AL. A continuous zoom lens with a focal length of 100 mm to 600 mm and a maximum lateral movement of 8.6 mm for AL has been designed, the max aperture of zoom lens is 150 mm, F number is 4, and the optical length is 349 mm.Through theoretical calculations and simulation analysis, the relationship between the on-axis aberration of AL and the xy polynomial coefficients of the AL is given. It is found that the aperture, lateral movement, and spacing are the main factors affecting the decentration of the AL aberration field center. Expanding the AL surface to a high-order xy polynomial to correct the aberration in the central field of view, the coma center moves to the center of the field, and there is no significant change in the symmetry centers of astigmatism and field curvature. Based on the characteristics of the aberration field center of AL and the principle of minimizing lateral movement, a five-component zoom lens is proposed, and the zoom equation is derived using the Gaussian bracket. A design example is given, with compact size and good imaging quality. The maximum lateral movement is 8.6 mm, allowing for a continuous zoom range from 100 mm to 600 mm, the small lateral movements are enabling fast zoom.