We propose and demonstrate a novel orientation-sensitive two-dimensional accelerometer based on fiber Bragg gratings inscribed in a multi-core fiber. Through monitoring of the wavelength shifts of three of the seven cores, including the central core and two outer cores which are not aligned in a straight line, information on vibration orientation as well as acceleration can be obtained simultaneously. Performance of the proposed accelerometer in terms of frequency, acceleration and vibration orientation are experimentally investigated. The designed two-dimensional accelerometer is capable of obtaining all these three parameters simultaneously. A sensitivity which is strongly dependent on the orientation is achieved, with a best orientation accuracy of 0.127° over a range of 0-180°. Moreover, the resonance frequency and the sensitivity can be optimized through adjusting the length and weight of the free-fiber. The ease of fabrication as well as the versatility of the proposed sensor makes it potentially useful in dynamic monitoring for industrial applications.