Optical zoom is an essential function for many imaging systems including consumer electronics, biomedical microscopes, telescopes, and projectors. However, most optical zoom imaging systems have discrete zoom rates or narrow zoom ranges. In this work, a continuous optical zoom imaging system with a wide zoom range is proposed. It consists of a solid lens, two Alvarez lenses, and a camera with an objective. Each Alvarez lens is composed of two cubic phase plates, which have inverted freeform surfaces concerning each other. The movement of the cubic phase masks perpendicular to the optical axis is realized by the actuation of the dielectric elastomer. By applying actuation voltages to the dielectric elastomer, cubic phase masks are moved laterally and then the focal lengths of the two Alvarez lenses are changed. By adjusting the focal lengths of these two Alvarez lenses, the optical magnification is tuned. The proposed continuous optical zoom imaging system is built and the validity is verified by the experiments. The experimental results demonstrate that the zoom ratio is up to 10×, i.e., the magnification continuously changes from 1.58× to 15.80× when the lateral displacements of the cubic phase masks are about 1.0 mm. The rise and fall response times are 150 ms and 210 ms, respectively. The imaging resolution can reach 114 lp/mm during the optical zoom process. The proposed continuous optical imaging system is expected to be used in the fields of microscopy, biomedicine, virtual reality, etc.