By using effective index method to calculate the transverse refractive index distribution of polymer rib waveguide,3D lightwave propagation is successfully simplified into a 2D one. Starting from the scalar wave equation,the one-step restriction on beam propagation is obtained by exploiting the slowly varying envelope and the paraxial approximation. The recursive formula is deduced using the series expansion of exponential differential operator,and the basic computing scheme is derived from the differential approximation. Considering the similar transformation of the symmetric matrix,the calculation speed of this algorithm is greatly improved. Based on the algorithm,the propagation characteristics of the TM lightwave in the Mach-Zenhder (M-Z) waveguide are systematically analyzed,including optical loss and the effect of structural parameters such as rib width,Y branch angle on the insertion loss. It is demonstrated that the operator expansion beam propagation method can be applied for the theoretical analysis and design of polymer M-Z waveguides with high precision,small computation complexity and high efficiency. The approach provides an alternative method for the design of polymer electro-optic modulators.