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Based on the B-P formula, Rusck formula and the Agrawal coupling model, we developed a time-domain method for lightning-induced voltages in overhead lines. Using this method, we studied the effects of different parameters on lightning-induced voltages and validated its accuracy using the 2-D FDTD method. The results show that: (1) The induced overvoltage generated by the first return current had a larger peak value and smaller wave head steepness. However, the induced overvoltage generated by the subsequent return current had a smaller peak value and larger wave head steepness. (2) Ground conductivity greatly influenced the amplitude and polarity of induced overvoltage. The peak value of induced overvoltage at the line centre negatively was correlated with ground conductivity. However, at the line end, the peak value of induced overvoltage positively was correlated with ground conductivity, and the waveform showed bipolar characteristics at poor ground conductivity condition (σ=0.001 S/m). (3) Both at the line centre and ends, the peak value of induced overvoltage increased with the line height. (4) Within distances from 50 to 1000 m from the lightning channel, the voltage waveforms calculated by our method were consistent with the 2-D FDTD results and the calculation error was less than 5%. In conclusion, because the calculation time of our method only needs 10 s with high calculation precision, it is very beneficial to be applied in lightning protection engineering.