The resistance relaxation in Au/SrTiO3/Au sandwiches with bipolar resistance switching has been investigated by the low frequency analysis. The power spectral density of the conducting current fluctuation in the high resistance state and the low resistance state shows 1/f behaviors. By contrast experiment, the low frequency noise for the high resistance state is ascribed to the Schottky barrier under reverse bias and the oxygen vacancy diffusion, while the noise in the low resistance state is due to the carriers fluctuation arising from the oxygen vacancy migration. The resistance relaxation can be further understood as the diffusion of oxygen vacancies under an electric field.