In order to minish the power loss of transitional bending waveguide and transitional grading waveguide, several shape functions of transitional waveguide are proposed and developed at first. Then they are simulated and analyzed by the finite-difference beam propagation method. Based on it, conditional relations between optimized transitional waveguide shape and the angle of transitional waveguide are found and proposed in math formula. During analyzing and calculating the power losses of transitional waveguide with different shapes with the finite-difference beam propagation methods, it is shown that the FD-BPM is perspicuous and convenient in simulating and analyzing optical waveguide device and units.