We propose and experimentally demonstrate the novel radio-frequency (RF) interrogation of a fiber Bragg grating (FBG) sensor using bidirectional modulation of a Mach-Zehnder electro-optical modulator (MZ-EOM). Based on the microwave photonic technique and active detection, the transfer function of the proposed system was obtained, and the time delay was calculated from the change in the free spectral range (FSR) at different wavelengths over the optimal measuring range. The results show that the time delay and the wavelength variation have a good linear relationship, with a gradient of 9.31 ps/nm. An actual measurement taken with a sensing FBG for temperature variation shows the relationship with a gradient of 0.93 ps/10 °C. The developed system could be used for FBG temperature or strain sensing and other multiplexed sensor applications.