We propose and experimentally demonstrate a novel real-time interrogation technique for a fiber Bragg grating (FBG) sensing system that is based on a frequency-shifted asymmetric Sagnac interferometer. FBG sensors are connected to the Sagnac loop by an optical coupler, and an acousto-optic modulator (AOM) is asymmetrically placed in the Sagnac loop. By linearly sweeping the driving frequency of the AOM, the environmental variation around each FBG sensor can be determined by measuring the spectrum of the interference signals of the two counterpropagating light beams reflected by the corresponding FBG. The system has the advantages of low cost and real-time sensing.