Herein, we propose a method for interrogating a fiber grating sensor using a dual-phase-shifted fiber grating and an optoelectronic oscillator (OEO). Combining the advantages of fiber grating sensing technology and microwave photonic technology, fiber gratings in a system serve both as sensing probes and as filtering units in a microwave photonic filter of the OEO. When the measurand changes the features of the sensing fiber grating, the frequency produced by the OEO also changes. This is not influenced by varying environmental temperatures, thus avoiding the cross-sensitivity problem of fiber grating sensors. Through the OEO, the wavelength change of the grating is reflected as a corresponding change in the microwave frequency. Furthermore, we experimentally demonstrate such a dual-passband microwave photonic filter using the phase-shifted fiber grating and construct an OEO ring based on the filter. Our experimental results show that the proposed system can provide an interrogation sensitivity of about 36 MHz/με. The implementation of this device holds promise for the development of a novel method of interrogating fiber grating sensors to achieve high-resolution and high-speed measurements. The proposed method can also help promote further developments in practical applications of optical fiber sensing technology.