In view of couples boundary node method and radial basis functions, a non-mesh method was presented to solve Poisson equation boundary value problems. In this method, the solution of original equation decomposed into a particular solution and a solution of laplace equation. Then, the particular solution was approximated by a series of radial basis functions, and the corresponding homogeneous solution was represented by means of boundary node method. After coupling the two expressions of the solution and forcing the boundary conditions, the equations were obtained to determine the unknown coefficients. Numerical examples are presented to show the efficiency of the presented method.