A compact in-fiber integrated fiber-optic Michelson interferometer based accelerometer is proposed and investigated. In the system, the sensing element consists of a twin-core fiber acting as a bending simple supported beam. By demodulating the optical phase shift, we obtain that the acceleration is proportional to the force applied on the central position of the twin-core fiber. A simple model has been established to calculate the sensitivity and resonant frequency. The experimental results show that such an accelerometer has a sensitivity of 0.09 rad/g at the resonant frequency of 680 Hz.