The invention discloses an optical fiber Bragg grating pressure sensor and a corresponding measurement method thereof, and the sensor comprises a housing, an elastic diaphragm, an L-shaped uniform strength beam and an optical fiber Bragg grating, wherein an opening is arranged at the top end of the housing, the opening and internal space of the housing constitute a cavity body, the elastic diaphragm covers the opening, the uniform strength beam is arranged in the cavity body, a pressure block is arranged at the free end of a beam arm of the uniform strength beam, a hard boss which is tightly connected with the pressure block is arranged on the lower surface of the elastic diaphragm, the optical fiber Bragg grating is mainly constituted by connecting two Bragg gratings with the identical temperature gradient in series through an optical fiber, and the two Bragg gratings are respectively connected on the upper surface and the lower surface of the beam arm. The sensor has the advantages that the elastic diaphragm is in rigid connection with the beam arm during the design, thereby not only improving the measurement precision, but also reducing the process difficulty; as the optical fiber Bragg grating is mainly constituted by the two Bragg gratings with the identical temperature gradient, the sensor can solve the temperature cross sensitivity problem during the measurement.