Accurate and reliable fault location method for alternating current (AC) transmission lines is essential to the fault recovery. MMC-based converter brings exclusive non-linear characteristics to AC networks under single-phase-to-ground faults, thus influencing the performance of the fault location method. Fault characteristics are related to the control strategies of the converter. However, the existing fault location methods do not take the control strategies into account, with further study being required to solve this problem. The influence of the control strategies to the fault compound sequence network is analyzed in this paper first. Then, a unique boundary condition that the fault voltage and negative-sequence fault current merely meet the direct proportion linear relationship at the fault point, is derived. Based on these, a unary linear regression analysis is performed, and the fault can be located according to the minimum residual sum function principle. The effectiveness of the proposed method is verified by PSCAD/EMTDC simulation platform. A large number of simulation results are used to verify the advantages on sampling frequency, fault resistance, and fault distance. More importantly, it provides a higher ranging precision and has extensive applicability.