A set of improved nonlinear coupled-wave equations describing the properties of fiber Raman amplifiers is developed, which can be applied to calculate the polarization dependent Raman gain. The mathematical model of the Raman gain in single-mode birefringence optical fiber is presented by coupling mode theory. The equivalence between the single-mode birefringence fiber Raman amplfiers excited at 45° with the fast axis by a linearly polarized pump and the practical fiber Raman amplfiers with randomly varying birefringence is discussed. A polarization dependent factor expressing the statistical properties of the polarization mode dispersion in single mode optical fibers quantitively is developed to substitute the one employed in the normal fiber Raman amplifier coupled nonlinear equations. The results of numerical simulations are accordant with the reported experimental data. The differences of the polarization dependent gains between the copropagating and counterpropagating pump are discussed.