This paper analyses bright and dark spatial self-similar waves propagation and collision in graded-index nonlinear waveguidc amplifiers with self-focusing and self-defocnsing Kerr nonlinearities.It finds an appropriate transformation for the first time such that the nonlinear Schr’6dinger equation (NLSE) with varying coefficients transform into standard NLSE. It obtains one-solitonlike, two-solitonlike and multi-solitonlike self-similar wave solutions by using the transformation. Furthermore, it analyses the features of the self-similar waves and their collisions.