Polymer rib optical waveguide is an important component in polymeric integrated optoelectronic devices such as electro-optic modulators. By using effective index method (EIM) to calculate the transverse refractive index distribution and effective index of polymer rib waveguide, the optical field distribution in each region is expressed as piecewise functions approximately. Based on the scalar wave equation that governs the guided modes,the variational parameter is determined by variational method (VM) for obtaining accurate transverse optical field distribution. The dispersion characteristics and transverse field distribution of the fundamental and higher-order modes are analyzed for polymer rib multimode waveguide. An algorithm is implemented to study the effect of the structural parameters and dimensions on the dispersion characteristics, and the optical field distribution of the fundamental and higher-order modes for TM modes is calculated. The single-mode transmission condition for polymer rib optical waveguide is obtained. The approach has advantages of high precision, small calculation complexity and high efficiency, which will provide theoretical reference and optimization method for the fabrication of polymeric electro-optic devices.