In this work, a novel fiber Bragg grating (FBG) sensor is designed for the measurement of motor axis transient torque. The sensing mechanism of FBG is introduced, the mathematical relationship between applied torque and Bragg wavelength is analyzed, and the theoretical model for a dual-FBG sensing structure is established. The two FBGs with different Bragg wavelengths are symmetrically attached onto the surface of the sensing axis, and used as sensing and reference elements, respectively. The structure can effectively relieve the thermal effect and eliminate environmental perturbation. After the calibration of axial torque with respect to Bragg wavelength by using a torque gauge, the measuring range of the fiber-optic torque sensor is 0~15 Nm, the sensitivity is 90.2 pm/Nm, the linearity is 0.9957, the repeatability error is 3.25 %FS, and the hysteresis error is 2.0 %FS. The torque sensing shaft is connected to the driving shaft of a stepper motor with a flexible coupling, and transient torque is obtained in real time with a frequency response bandwidth of <35 kHz, which is limited only by the readout speed of the interrogation system. This work provides a new technique for transient torque measurement of a motor.