In this paper, we introduce non-invasive Gaussian-enveloped linear chirp (GELC) reflectometry for the diagnosis of live underground power cables. The GELC reflectometry system transmits the incident signal to live underground power cables via an inductive coupler. To improve the spatial resolution of the GELC reflectometry, we used the multiple signal classification method, which is a super-resolution method. An equalizer, which is based on Wiener filtering, is used to compensate for the signal distortion due to the propagation characteristics of underground power cables and inductive couplers. The proposed method makes it possible to detect impedance discontinuities in live underground power cables with high spatial resolution. Experiments to find the impedance discontinuity in a live underground power cable were conducted to verify the performance of the proposed method.