A general and simple semianalytical method based on the Galerkin procedure is introduced in this letter for wave propagation problems related to radially inhomogeneous cylindrical dielectric waveguides with arbitrary permittivity profiles. The complicated wave propagation problem in an inhomogeneous waveguide is transformed into a simple problem of solving an equivalent matrix in terms of the Galerkin procedure. Eigenvalue solutions are given for three kinds of representative radially inhomogeneous cylinders to verify the generality of the proposed semianalytical method. The accuracy and the improvement of the convergency are illustrated by comparing the calculated results with those obtained by the analytical method or the matrix numerical method.@en