High-voltage complex cable lines fault location process is complicated,and the fault pinpointing method and accuracy need to be improved. The positioning method based on time difference of arrival (TDOA) is presented in this paper. Mathematical model for multi-sonic TDOA is established. And the objective function of the optimal solution of nonlinear equations for two-dimensional fault location is derived. The objective function is optimized by Broyden-Flether-Goldfarb-Shanno (BFGS) quasi-Newton algorithm. The algorithm has fast convergence speed and facilitates digital processing. The validity of the method is verified by MATLAB simulation analysis and positioning experiments. The proposed fast and accurate method can be used for high-voltage complex cable lines fault pinpointing.