High-temperature superconductor (HTS) current leads are important components of the EAST and CFETR tokamaks, which are responsible for operating the high parametric current. HTS current leads are made of Bi-2223/Ag-Au alloy tapes, which have the characteristics of slow quench propagation speed and weak quench signal. Traditional thermometers are easily damaged by the high voltage from the current leads, and the terminal voltage signal cannot reflect the hot spot changes of current leads in real time. In this paper, a novel quench detection method based on optical frequency domain reflection technology is proposed. Temperature variations of HTS can be obtained in real time by demodulating the Rayleigh scattered spectrum from the distributed optical fiber attached to the surface of HTS stacks. This paper describes a quenching experiment for one pair of 1-kA small current leads. The external thermal disturbance is increased to explore the quench propagation of HTS current leads under the condition of a self-field, 77 to 80 K air and conduction combined cooling method. From the experimental results, the temperature distribution map of the whole HTS lead is obtained. Compared with the quench voltage, the spectral shift of the fiber appeared to be about 2 s ahead, and the hot spot position can be located with 1-cm accuracy.