From the positive-sequence network, a new fault location method based on a lumped parameter model is proposed for single-circuit three-terminal transmission lines. This method includes two stages, including fault branch determination and fault position calculation. At the fault branch determination stage, the fault branch determination function is deduced and designed without considering the line-to-ground capacitance – this to simplify this function. From the opposite signs between the function values at both ends of each branch, the fault branch can be determined. In addition, to ensure the accuracy of fault branch determination when faults occur near the branch head-end and T-node, the fault branch criterion is also given. At the fault position calculation stage, the effect of the line-to-ground capacitance is considered to ensure the accuracy of the calculation. Then, an analytical expression of fault distance is given based on positive-sequence component and positive-sequence fault component. Based on this expression, the fault distance can be solved by only several iterations. The proposed method is applicable to various types of faults, and it is suitable for high-resistance faults near the T-node without dead zone. Moreover, the method has low computational overhead, which makes it easy for programming. Theoretical analysis and simulation tests show that the effectiveness and accuracy of the proposed method are not affected by fault location, transition resistance or T-junction position. This work is supported by the Joint Project of Commission of National Natural Science Foundation of China-Smart Grid of State Grid Corporation of China (No. U2066210).