Acquiring medium- and high-frequency acceleration signals is vital for broad infrastructure health monitoring, such as bridges, railways, and tunnels. This article introduces an innovative fiber Bragg grating (FBG) accelerometer featuring a V-shaped flexure hinge structure with enhanced sensitivity. Theoretical calculation and simulation analysis software were employed to evaluate the proposed structure's parameters. Experimental results show a sensitivity of approximately 67.9 pm/G under a working bandwidth of 400–900 Hz and a resonant frequency of 1250 Hz. The influence of temperature at 8.4 pm/°C and transverse interference validate 3.5%. These findings align with simulations, affirming the sensor's performance. This innovation holds promise for enhancing structural integrity monitoring in large-scale structures by detecting medium- and high-frequency vibration measurements.