To ensure the imaging quality of the zoom lens, the image plane stabilization should be maintained, while the aberration is corrected. Mechanical compensation can ensure the accuracy of the cam, accomplish the image plane stabilization and keep the imaging quality. With dynamic optical theory, the image motion compensating group formula of the zoom optical system is derived, and the trace curve of the image motion compensating group is plotted. With the plotted curve the cam is fabricated, and compensates the image motion caused by the zoom of the optical system totally. The design for three zoom systems is presented, Which validates the validity and the practicability.