Accurate and rapid fault localization for transmission line faults is essential for power system protection and maintenance. In this paper, a PMU-based algorithm for locating transmission line faults is proposed. By employing Principal Component Analysis (PCA) method on line current time series data, fault region is firstly identified. The pre-fault and during-fault positive sequence voltage measurements are then utilized to estimate unknown bus voltages through least square method and therefore determine exact fault location within the fault region. Different fault resistances and four types of fault, namely, single line to ground fault, double line to ground fault, line to line fault and three-phase balanced faults are used to evaluate the effectiveness of the method on the IEEE 14-bus system as well as the IEEE 30-bus system. Additionally, the impact of noise on PMU measurements is investigated to assess the robustness of the proposed method.