To enhance the sensitivity of the in-fiber Bragg grating (FBG) sensor is one of the effective ways to improve the resolution of the FBG sensing system. Based on effect of FBG stress sensitivity enhancement by encapsulating the FBG with elastic polymer and a metal bellows, a novel model of high-sensitivity FBG pressure sensor is proposed. The relation between relative shift of Bragg wavelength and the pressure applied on the sensor is derived, and the analytical expression of pressure sensitivity coefficient is also given. It indicates that the relation between the relative shift of Bragg wavelength and applied pressure is linear, and the pressure sensitivity coefficient can be enhanced by properly selecting the parameters of the elastic part and the metal bellows, such as the elastic modulus of the elastic part and the elastic constant of the bellows, and the size of them. The experimental pressure sensitivity coefficient of the sensor is -4.35×10-9 Pa-1 (-6.74 nm/MPa), which is 2197 times of that of the bare FBG, the theoretical value of the sensor is -4.6×10-9 Pa-1, they fit very well.