Abstract: The propagation property of Gaussian beam traveling through graded-index media with Kerr nonlinearity is investigated using the aberrationless theory of self-focusing. Expressions for the spot size and the beam radius of curvature of Gaussian beam are obtained. It is shown that the propagation property of Gaussian beams depends on the competition between the diffraction effect and the combined effect of nonlinearity and graded-index. The graded-index tends to shorten the self-focusing distance.