The characteristics of the radio-frequency unbalanced Mach-Zehnder interferometer (RF-UMZI) for wavelength demodulation of the fiber Bragg grating (FBG) sensors are studied. The final output power loss of this RF-UMZI due to the incoherent beam loss, insertion loss, and reflection bandwidth of FBG are measured in the experiment. For a certain amount of sample observations of the intensity with a certain microwave frequency, a complete method using the maximum RF intensity discrimination for data processing is proposed. The maximum intensity of each frequency is mapped to obtain the frequency response for notch frequency, and a sensitivity of 0.1692 dB/℃ at 119.96 MHz is obtained. This experiment is of practical reference value in performance improvement and feasibility study for incoherent light and microwave photonics filter utilizing in fiber sensing.