Microwave photonic (MWP) sensing and measurement are envisioned to be a promising alternate to the conventional pure electronic or optical solutions. By using a semiconductor laser (SL) subjected to external optical feedback (EOF) operating at period-one (P1) dynamic state to generate MWP signals, a high performance sensing system is proposed for displacement with wide measurement range and super-high resolution. Through analysis on the state diagram of the system and its dynamics in P1, the relationship between the relaxation oscillation frequency of the system and external cavity length is determined. Further, a measurement formula for displacement sensing is worked out. Then, the relevant signal processing algorithm to retrieve displacement information is developed by considering mode-hopping, frequency-hopping, and sawtooth-like phenomena that occurred in the relationship. Both simulation and experiment results confirmed the proposed MWP sensing approach.