With external optical feedback (EOF), a laser diode (LD) can operate at different dynamic states. In this work, an LD with EOF is set at period-one (P1) oscillation state to generate microwave photonic (MWP) signal for sensing. Firstly, the P1 state boundary of the LD is determined and then the influence of the LD controllable parameters on the boundary is studied by solving the well-known Lang-Kobayashi equations. A set of parameters selection rule for designing an LD based MWP sensing system is obtained. In addition, a measurement algorithm for recovering the displacement from an MWP sensing signal is developed. By making full use of the sensing information carried in both amplitude and frequency of the MWP signal, displacement sensing with high resolution and large range can be achieved. Both simulations and experiments are conducted to verify the proposed method and show it is capable of realizing wide measurable range, high measurement sensitivity, and high resolution sensing.