A novel structure of F-P cavity optical fiber pressure sensor was proposed. Based on Fabry-Perot interference, the sensor uses the longitudinal deflection of the pressure sensitive membrane to drive the lateral displacement of the displacement column to change the cavity length. The design method of the sensor and its working principle were described in detail, and the influence of different parameters on the sensor performance was analyzed. The deflection of the pressure sensitive diaphragm under pressure was simulated by ANSYS software. Combined with the existing MEMS technology, MEMS fiber pressure sensors with the characteristics of simple process, low temperature coefficient, high sensitivity and anti-electromagnetic interference can be produced.