Ritz-Galerkin method is used only for obtaining propagation constant and the radial mode field in core region of graded-index optical fibers. Cladding field has been constructed by using the accurate functional form(modified Bessel function) with two approximate parameters: the transverse decay constant in the cladding and the field value at core-cladding interface,which are already known. Numerical results show that the improvement on accuracy is significant. This approximate Ritz-Galerkin method has been applied to the calculation of coupling coefficient between two step-index optical fibers. Results are agreed well with exact values.