Fiber optic sensors based on the Fabry-Perot (F-P) interferometer have been widely used because of its simple structure, small size, and high sensitivity. The refractive index of liquid can be measured by the open F-P interferometer. We can make an open F-P interferometer through mechanical cutting, femtosecond laser breakdown and some other methods. An open F-P interferometer sensor is fabricated with an open hollow capillary and two segments of single-mode fibers welded together by glass flux. Absolute measurement of refractive index of liquid can be achieved when the cross-correlation signal processing technology is used. Refractive index measurement experiments are performed for NaCl solutions with different concentrations. The measurement resolution for refractive index can reach 10-5 RIU magnitude, and the temperature sensitivity of the sensor is 39.59 nm/℃.