This paper proposes a design method for a fiber Bragg grating (FBG) displacement sensor with a hyperbolic flexible hinge structure. A compact FBG displacement sensor with strong micro displacement measurement capability was fabricated. The final assembly testing showed that the sensor achieved good linearity with a linearity of 0.53%F·S at a range of 50 mm. The sensitivity was measured as 24.45 pm mm−1, hysteresis error as 1.1%FS, and repeatability error as 0.659%. The testing results demonstrated that the fabricated FBG displacement sensor exhibited strong practicality and good stability, making it suitable for long-term displacement monitoring of slope safety.