Optical system of zoom lens with image stabilization

An optical system of a zoom lens is provided. The optical system of the zoom lens includes thirteen lenses which are divided into four lens groups, wherein: the zoom lens comprises in a following order from a subject: a first lens group which has a positive refractive index; a second lens group which has a negative refractive index, and moves along an optical axis; a third lens group which has a positive refractive index; and a fourth lens group which has a positive refractive index, wherein the first lens group comprises four lenses, and an external surface of a first lens is concave in a direction of a plane of an image; the third lens group comprises two meniscus lenses which are concave toward an image plane, and is made with capability of cross-section displacement relative to an optical axis; and the fourth lens group is convex-concave glued lens.