Crossing waveguide is an important unit in integrated optics. The generalized Douglas (GD) scheme for variable coefficients is applied to wide-angle multistep finite-difference beam propagation method (FD-BPM). Aiming at the structure and refractive-index profile of wide-angle cross waveguide, the optical field distribution has been calculated by the method. Compared with Crank-Nicholson (CN)scheme in the same computational time and resource, the method has two characteristics