The fault information in grounding electrode lines is weak and well-hidden, making detection and fault location very difficult. Based on this, a new single-ended fault location algorithm for grounding electrode lines is proposed, utilizing broadband excitation injection and the short-time matrix pencil method (STMPM). First, a Gaussian signal excitation with an “oscillatory decay characteristic” is injected into the grounding electrode line in differential mode, ensuring that the injected excitation does not leak into the DC system side through the neutral bus and minimizing waveform distortion during the propagation of the signal along the grounding electrode line, thereby improving the detection efficiency of fault traveling waves. Secondly, sliding short-time windows are used to perform singular value decomposition (SVD) on the fault traveling waves. The eigenvalues obtained from the decomposition are used to distinguish between interference signals and fault signals, effectively amplifying the weak fault signals while suppressing the interference signals. Finally, the damping factor of the fault traveling wave within the short window is determined, establishing a one-to-one mapping relationship between the zero-crossing moment of the damping factor and the arrival time of the fault traveling wave, and the fault distance is then determined. Extensive simulations show that the distance measurement algorithm can effectively detect fault traveling waves and achieve high fault location accuracy.