Using the coupled nonlinear Schrödinger (CNLS) equation containing the Raman gain, the Duffing equation with Raman gain is derived, which is represented by the Stokes parameters, and then the elliptic integrals are used to compute the analytical solutions. This article focuses on the analysis of the Raman gain influence on the evolution of the polarization state when the optical waves are propagating in a low-birefringence fiber. Results show that the transmission cycle of the polarization evolution state can be changed due to Raman gain, if the input power and motion constants have a certain relationship.