In the WKB analysis, we propose the new forms of the trial eigenfunctions which not only converge at the turning points but also approximate to the conventional WKB solutions away from the turning points. The eigenvalue equation of multiple waveguides with graded index profile are derived by using the proposed WKB analysis and the transfer matrix method. The drived equation sare represented in the recursive form. The results of the eigenvalue equation sare comapred with those of the FDM, one of the well-known computational methods, for a three-waveguide coupler.