Most existing quench protection methods can only detect the overall quench fault, and cannot effectively reflect the local quench fault. Therefore, given the peak characteristics of the temperature waveform along the conductor layer after the local quench of the superconducting cable, a local quench detection and protection method for a superconducting cable based on distributed optical fiber temperature measurement technology is proposed. The method uses a fiber optic system to measure the temperature along the conductor layer of the superconducting cable, a Gaussian filter to filter out the noise in temperature data, and identifies the upper and lower edges of the wave peaks in the temperature waveform by a multi-resolution Morphological Gradient (MMG). Then the local quench heat-generating zones are calculated and determined. Finally, alarm and tripping are carried out according to the size and temperature rise of the quench heat-generating zones. Simulation results show that the proposed method has good anti-noise performance, can accurately detect and judge the quench heat-generating zones and quench fault severity, and effectively ensure the operational safety of the superconducting cable. This work is supported by National Natural Science Foundation of China (No. 51677080) and Science and Technology Project of Shenzhen Power Supply Bureau Co., Ltd. (No. 090000KK52170171).