In this paper, a high-fineness optical fiber Fabry-Perot (F-P) pressure sensor based on micro-electro-mechanical system (MEMS) is proposed and experimentally demonstrated. The sensor is a high-fineness F-P interferometer formed by a silicon diaphragm and a Pyrex#7740 glass sheet both coated with high-reflection film. The change of pressure causes the length change of F-P cavity. Thus, based on the high-sensitive optical fiber white light interferometry, the pressure can be obtained by measuring the cavity length of the F-P. Experimental results show that the pressure sensor has properties of good measurement resolution, high linearity and low temperature drift characteristics.