Alvarez lenses can realize a large zoom ratio with minimal lateral movement. We analyzed the movement sensitivity in the - and -directions. An polynomial model was used to describe the wavefront error introduced by the Alvarez lens decenter in the - and -directions. A optical zoom system was developed with two pairs of Alvarez lenses and was used to verify the theoretical analysis results. The tolerance analysis result for the optical system is consistent with the theoretical analysis. The results showed that it is sensitive to Alvarez lens decentering, especially in the direction perpendicular to the movement direction.