To address the high cost of installing fault location terminals and the complexity of wavefront identification in multi-branch distribution network lines, a fault location method based on time-domain differential operation is proposed. First, the line-mode component of the fault-induced voltage traveling waves is expressed as an exponentially decaying component superimposed on a sinusoidal waveform within a specific time window. By applying a time-domain differential operation, the sinusoidal component is eliminated, thereby transforming the fault traveling wave into pulse signals. Furthermore, temporal sequence constraints for the fault reflection waves are established to accurately identify the arrival times of the wavefronts when faults occur on different branches. Finally, various fault scenarios are simulated and validated in MATLAB/Simulink. The results indicate that the proposed method can achieve accurate fault localization with traveling-wave acquisition devices installed only on the main line. The method exhibits minimal sensitivity to variations in fault type, initial inception angle, and fault resistance, demonstrating excellent reliability and cost-effectiveness.