To provide a zoom lens system with a vibration reduction having a long back focal length suitable for a digital SLR camera, a high zoom ratio, and a wide angle of view of 70° or more. The system includes, in order from the object, a first positive lens group, a second negative lens group, a third positive lens group, and a fourth positive lens group. Upon zooming from wide-angle end state to telephoto end state, a distance between the first and second lens groups increases, a distance between the second and third lens groups decreases, and a distance between the third and fourth lens groups varies. The third lens group is composed of a positive front lens group and a negative rear lens group. Image plane correction upon camera shake can be performed by shifting only the rear lens group substantially perpendicularly to the optical axis. Given conditions are satisfied.