A novel high precision fiber Bragg grating (FBG) pressure sensor is proposed. The sensor is based on the structure of elastic diaphragm. The pressure sensing FBG (PS FBG) is connected directly to the diaphragm. Axial displacement occurs under pressure and compresses the PS FBG to realize pressure measurement. The temperature compensating FBG (TC FBG) departs form the diaphragm. So it is insensitive to external pressure. Both FBGs are applied with certain pretensions. Therefore, their response to environmental temperature is nearly the same. Accordingly, real-time temperature compensation can be realized. Without strain delivery among structures, the proposed sensor responses to external pressure immediately and ensures a high precision measurement. In the experiment, the pressure measurement fluctuation of the sensor is less than ±0.7%F.S. during temperature variation. The pressure precision reaches 0.19%F.S. in the rage of 25 MPa.