The symmetric directional coupler with optical rib waveguide is simulated using a novel three-dimensional beam propagation method (3D-BPM) based on the Galerkin method. The coupling ratio is as high as 99.4%. The matrix derived from the present method is small. Consequently, the calculation is efficient. A tangent-type function is applied to map the infinite region into a closed region. As a result, the artificial boundary conditions are eliminated.