An orientation-dependent optic-fiber accelerometer based on the excessively tilted fiber grating (ExTFG) inscribed in SM28 fiber is demonstrated, which is based on the optical power demodulation scheme. Without any complicated processing, the cladding mode resonances of the bare ExTFG show high sensitivity to slight perturbation of bending. Due to its excellent azimuth-related bending properties, such a bare ExTFG fixed on a simple cantilever beam has exhibited strong orientation-dependent vibration properties. The experimental results show that a TE mode of the sensor can provide a maximum acceleration sensitivity of 74.14 mV/g at 72 Hz and maximum orientation sensitivity of 9.1 mV/deg while, for a TM mode, a maximum acceleration sensitivity of 57.85 mV/g at 72 Hz and maximum orientation sensitivity of 7.4 mV/deg could be achieved. These unique properties enable the sensor to act as a vector accelerometer for applications in many vibration measurementfields.