The basic idea of the finite element beam propagation method (FE-BPM) is described. It is applied to calculate the fundamental mode of a channel plasmonic polariton (CPP) waveguide to confirm its validity. Both the field distribution and the effective index of the fundamental mode are given by the method. The convergence speed shows the advantage and stability of this method. Then a plasmonic waveguide with a dielectric strip deposited on a metal substrate is investigated, and the group velocity