In this paper, a study of the ray propagat ng through nonoylindrioal defocusing GRIN lens is presented. A set of general solutions of the paraxial merdial ray equation for nonoylindrioal defocusing GRIN lens which meet the weakly inhomogeneous condition (ie,d/(dz)[g-1 (z)]≤1) is proposed. The refractive-index profiles are derived from the condition met by the qiadient parameter-g(z), which provides the analytical solutions of the ray equation. Two independent analytical solutions for ray propagating paths are given and the paraxial imaging characteristics are discussed for a parabolic defocusing GRIN lens.