The polarization dependences of gain and amplified spontaneous Brillouin scattering (ABS) noise for fiber Brillouin amplifier (FBA) are analyzed through theories, simulations, and experiments. Modified vector propagation equations for calculating the gain of the probe signal and the ABS noise are derived and analyzed in the Stokes spaces. In simulations and experiments, we prove that the gain of the probe signal and the ABS noise are strongly dependent on the relative state of polarization (SOP) of the pump and probe signals. The closer the relative SOP of the pump and probe signals is, the more obvious ABS noise suppression effect will be brought by increasing the power of the input probe signal.