We demonstrate a linearly-polarized, ytterbium-doped fiber laser that uses an uncoated, undoped ceramic YAG plate as the output coupler, and the corresponding polarization extinction ratio of laser beam increases with incident pump power and then saturates at larger pump power. For comparison, the output coupler of the fiber laser is replaced by 10% reflectivity plane mirror, while the feature of the polarization of laser output is kept unchanged. The results show that the origin of the pump-dependent and self-started polarization is associated with the intensity-dependent nonlinear birefringence in the gain fiber. We demonstrate a linearly-polarized, ytterbium-doped fiber laser that uses an uncoated, undoped ceramic YAG plate as the output coupler, and the corresponding polarization extinction ratio of laser beam increases with incident pump power and then saturates at larger pump power. , the output coupler of the fiber laser is replaced by 10% reflectivity plane mirror, while the feature of the polarization of laser output is kept unchanged. The results show that the origin of the pump-dependent and self-started polarization is associated with the intensity-dependent nonlinear birefringence in the gain fiber.