Since most of the Extra High Voltage (EHV) transmission lines are untransposed and multi-circuits, errors are occurred inevitably because of the unbalanced impedances of the lines and so on. Therefore, a distance relaying algorithm applicable to the untransposed multi-circuits transmission lines needs to be developed. The proposed algorithm of fault location estimation in the paper uses the fundamental phasor to reduce the effects of the harmonics. This algorithm also analyzes the second-order difference of the phasor to calculate the traveling times of waves generated by faults. The traveling time of the waves generated by faults is derived from the second-order difference of the phasor. Finally, the distance from the relaying point to the faults is estimated using the traveling times. To analyze the performance of the algorithm, a power system with the EHV untransposed double-circuit transmission lines are modeled and simulated under various fault conditions such as several fault types, fault locations, fault inception angles and fault resistances. The results of the simulations show that the proposed algorithm has the capability to estimate the fault locations quickly and accurately.