A highly localized eccentric fiber Bragg grating (EFBG) accelerometer was proposed, and its orientation-dependent measurement results were demonstrated experimentally. An EFBG was inscribed point-by-point (PbP) in a single-mode fiber (SMF) using a femtosecond laser, and the cladding mode was recoupled to excite the ghost mode through an abrupt taper. Owing to the asymmetry caused by the lateral offset of the EFBG, the ghost mode showed a significant directional response to acceleration. Furthermore, monitoring the fundamental core mode resonance can help calibrate accidental power perturbation or cross-sensitivity.