We consider propagation of surface TE waves in the Goubau line (GL) assuming that the dielectric cover is non-linear and inhomogeneous. The problem at hand is reduced to a non-linear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating TE waves for the chosen nonlinearity (Kerr law) is proved by the method of contraction. Conditions under which several higher-order waves can propagate are obtained, and the intervals of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiment two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation modes are found.