This paper presents a high-sensitivity fiber Bragg grating (FBG) displacement sensor with a novel configuration for structural health monitoring. The transverse movement of an optical fiber that has been configured as a tight suspension status with its two ends fixed has been utilized to measure displacement. The theoretical models for both static and dynamic displacements have been derived. The corresponding simulations have been conducted to determine the relationship between the model parameters and the sensor performance. This approach supports the sensor design improvement and structural optimization. Two small working ranges have been selected to determine the simplified linear model according to Taylor series. The sensitivity of this sensor can reach up to 490.1 pm/mm with a high resolution of 2.04 μ m in a range of 1.4~2.0 mm. The introduction of the supporting spring unit has significantly enhanced the sensor’s resonant frequency without sacrificing the sensitivity. The application of the stiffer spring unit has enlarged the working bandwidth from 0~8 Hz to exceed 50 Hz. Enhancing the damping ratio unit can effectively improve the flatness of the dynamic response within the working bandwidth, while it does not affect other dynamic properties of the sensor. These improvements and design guidelines have been validated by both dynamic experiments and theoretical modelling.