This work is about a suitable numerical method based on the Muntz-Legendre polynomials for solving a type of the generalized Abel integral equations. The propose method approximates the unknown function with the Muntz-Legendre polynomials. To do this, we apply these functions and using Muntz-Galerkin method for the numerical solutions of this problem. Also, the stability and uniqueness of the solution by this scheme will be shown. Moreover, the convergence of this algorithm will be proved by preparing some theorems. Several numerical examples are presented to show the superiority and efficiency of current method.