To address the fault location challenges in 35 kV distribution networks caused by insufficient sensing and measurement capabilities and the complexity of branched lines, a time-domain impedance method based on single-ended measurement is proposed. First, tailored to the characteristics of phase-to-phase short-circuit faults in 35 kV branched distribution networks, a fault location model based on single-ended measurement is established. The fault location equations based on the time-domain differential equations of the post-fault loop is derived. Then, the fault distance, branch current, and transition resistance in the fault location equations are treated as unknown parameters, a nonlinear solution is obtained using the Levenberg-Marquardt algorithm (LMA). Fault localization is then performed sequentially on each line segment and branch to determine the fault location through a step-by-step search method. Finally, a 35 kV network model is built in PSCAD to verify the reliability and accuracy of the proposed algorithm. This method requires only the phase current and phase voltage measurements at the substation feeder without the need for additional equipment, and can achieve precise fault distance calculation and effective identification of the faulted branch.