Abstract In this work, a new solution to the partial differential Maxwell equations is first derived to investigate all polarization conversions of the transverse and the longitudinal components of guided-modes in a bending waveguide. Then, for the silica-waveguides, the polarization conversion efficiencies are numerical calculated and a significant finding is that the transverse–longitudinal polarization conversion efficiency is much higher than that of transverse–transverse polarization conversion. Furthermore, the dependences of all the conversion efficiencies on waveguide parameters are found. The agreeable results between the numerical calculation and the finite difference time-domain (FDTD) simulation show that for two 100 μ m long bending waveguides of 0.75 and 1.50% index contrasts, the amplitude conversion efficiencies from ∼ 10−3 to ∼ 10−2 can be realized for the transverse–transverse polarization components and that of ∼ 10−1 can be realized for the transverse–longitudinal polarization components.