Multi-dimensional acceleration sensors are used in important applications in the aerospace, weapon equipment, and nuclear fields and have strict requirements in terms of performance, volume, and mass. Fiber Bragg grating acceleration sensors use optical wavelength signals as a medium for information transmission to effectively eliminate the influence of electromagnetic interference between multi-dimensional sensors. In this study, we designed a composite flexure hinge three-dimensional acceleration sensor. To this end, we investigated the coupling mechanism between a new integrated elastomer structure and fiber grating to determine the influence of structural parameters on the static and dynamic characteristics, volume, and mass of the sensor. By optimizing the strain distribution, amplitude, and frequency and coupling characteristics between dynamic dimensions, a design theory and a method for integrating the three-dimensional acceleration sensor were developed. The size of the optimized accelerometer is only 25 mm × 25 mm × 30 mm. Performance testing revealed that, along the three spatial dimensions, the sensor had sensitivities of 51.9, 39.5, and 20.3 pm/g, respectively, resonance frequencies of 800, 1125, and 1750 Hz, respectively, and a measurable frequency range of 0–250 Hz.