Abstract: Based on the aberrationless theory of self-focusing,the closed-form propagation expressions for Gaussian beams through a nonlinear gradient-index medium are derived by means of the ABCD law.By using the matrix optics method,the propagation properties of Gaussian beams through a nonlinear gradient-index lens are studied.It is shown that the nonlinearity and inhomogeneity of the medium,laser power and input beam parameter affect their propagation properties.