A novel inertial measurement unit (IMU) was proposed to measure the three-axis linear/angular acceleration of a body using six fiber Bragg grating (FBG) optical fiber acceleration sensors sharing the same rotational center. The six acceleration sensors were shown to accurately distinguish between movements in different directions using a vibration generator and rotary motor/encoder device. The results also indicated that the measurement range of the FBG linear acceleration sensor was ±14 g, its average sensitivity was approximately 229.4 pm/g, and its nonlinearity was under 0.05%. Furthermore, the average sensitivity and nonlinearity of the FBG angular acceleration sensor were 21°/s²/pm and 0.23%, respectively. When measuring linear and angular acceleration, the cross-axis sensitivity of the IMU was within 2.0%. The measurement accuracy of the roll and pitch angle during 360° rotation as well as that of the yaw angle during 720° rotation were both in the range of 0.54 to 1.31%. Most of results indicated that the FBG-based IMU sensor was within the performance specifications of an equivalent conventional IMU sensor. Thus, the concept underlying the proposed sensor can be confidently used as a basis to develop a high-precision IMU sensor that is unaffected by electromagnetic interference.