In this paper, we propose and demonstrate a novel Tilted Fiber Bragg grating (TFBG) sensing demodulation scheme based on microwave photonic technique. In the proposed approach, the optical power spectrum from BBS (Broadband source) is shaped by a TFBG and then sent to a dispersive element to perform the linear wavelength-to-time mapping. A nonuniform microwave photonic filter with the center frequency depending on the shaped optical spectrum is obtained at the output of a high-speed photodetector. The central frequency and the envelope of the generated microwave photonic filter will shift according to the change of environment. Theory and a proof-of-principle experiment are implemented to verify the proposed approach.