An interferometric structure based on a Dual-Resonance Long-Period Grating (DRLPG) within a Fiber Loop Mirror (FLM) is presented in this paper. Its purpose is to measure the refractive index (RI) of liquid analytes. The grating is the RI sensing probe, while the FLM serves as a band-pass filter. Due to the high extinction ratio of the FLM, amplitude measurements can be obtained, allowing implementation of the differential interrogation method to establish the sensitivity of the device. The use of a polarization controller makes it possible to fine-tune the interferometric peaks with respect to the two notches of the DRLPG. Precisely aligned configuration produces a maximum sensitivity of 3871.5 dB/RIU within the RI range of 1.3333 up to 1.3419 with linear sensor response.