Precision displacement of less than a few nm resolution was measured in real-time using fiber optic EFPI sensor. The novel method for real-time processing of analyzing EFPI output signal was developed and verified. Linearity in the mean values of interferometric light intensity among adjacent fringes was shown and verified the sinusoidal approximation algorithm that estimates past and coming fringe values. Real-time signal processing program was developed and the intensity signal of the EFPI sensor was transformed to the phase shift with this program. The resolution below $0.36{sim}8.6$ nm in the displacement range of $0{sim}300{mu}m$ was obtained. The nano-positioner with a piezoelectric actuator and the EFPI sensor system was designed and tested. The positioner successfully reached to the desired destination within 1 nm accuracy.