Backscatter noise is a key limiting factor in the performance of resonant fiber optic gyroscopes. To enhance the accuracy of resonant fiber optic gyroscopes, a gyroscope system based on sideband locking technology is proposed. In this scheme, two tunable semiconductor lasers independently provide the clockwise and counterclockwise optical paths. An optical phase-locked loop is employed to achieve independent subharmonic phase locking of the two output lights, with their optical frequency difference equaling one free spectral range (FSR). By applying sinusoidal modulation at different frequencies to generate sidebands, the sideband locking technique is used to lock the first-order sidebands of the two lights to adjacent resonant frequencies. Through the filtering effect of the fiber ring resonator, the carrier intensity of the transmitted light and other sidebands are effectively suppressed. With this signal processing technique, the influence of two types of backscatter noise is completely eliminated, and the additional suppression of laser frequency noise is achieved. Experimental results show that, based on the Allan deviation, the bias instability of the gyroscope output is 1.42°/h. This method significantly improves the detection accuracy of the resonant fiber optic gyroscope under the same parameter precision or device performance requirements.