In this paper, a novel fiber Bragg grating sensing system based on thin-film lithium niobate ridge waveguide micro-nano structure is proposed, with the core device integrating an electro-optic Bragg deflection modulator based on an unbalanced Mach-Zehnder interferometer. The wavelength demodulation is accomplished by converting the shift of the central wavelength of the Fiber Bragg Grating into phase modulation using an unbalanced Mach-Zehnder structure and achieving intensity modulation by electro-optic modulation. Using the finite element method, the half-wave voltage of the unbalanced Mach-Zehnder interferometer is 29.4 V, the demodulation efficiency is 2.03 V·cm, and the extinction ratio of the device is greater than 54 dB when the center wavelength is 1.55 μm. The maximum diffraction efficiency of the electro-optic Bragg deflection modulator is 68%, which is much higher than the diffraction intensity required by this system. With the on-chip integrated design, the system effectively reduces the size and transmission loss compared with the traditional demodulation system. At the same time, it performs excellently in the external 10 kHz dynamic signal test, demonstrating its great potential for application in high-frequency strain measurement.