The accurate estimation of a fault location is desired in distance protection schemes for transmission lines in order to selectively deactivate a faulted line. However, a typical method to estimate a fault location by calculating impedances with voltages and currents at relaying points may have errors due to various factors such as the mutual impedances of lines, fault impedances, or effects of parallel circuits. The proposed algorithm in this paper begins by extracting the fundamental phasor of the positive sequence currents from the three phase currents. The second-order difference of the phasor is then calculated based on the fundamental phasor of positive sequence currents. The traveling times of the waves generated by a fault are derived from the second-order difference of the phasor. Finally, the distance from the relaying point to the fault is estimated using the traveling times. To analyze the performance of the algorithm, a power system with EHV(Extra High Voltage) untransposed double-circuit transmission lines is modeled and simulated under various fault conditions, such as several fault types, fault locations, and fault inception angles. The results of the simulations show that the proposed algorithm has the capability to estimate the fault locations with high speed and accuracy.