At present, in the theoretical calculations and researches of coupled lightning overvoltage of transmission lines, most of them consider the situation of single return stroke current source and ignore that lightning mainly exists in the form of multi-pulse in reality. Many studies ignore the influence of conductor corona discharge effect on overvoltage suppression. Therefore, this paper improves the double Heidler return stroke current source, establishes a multi-pulse current source with three peak-currents in one discharge process, and optimizes the corona discharge model under single pulse to meet the corona discharge effect under multi-pulse. At the same time, the leap-frog algorithm is used to make the second-order high-precision difference of Maxwell equations to improve its model stability. The results show that the relative error between the overvoltage peak calculated in this paper and the IEEE standard result under the action of single pulse is only 2.11%. At the same time, the line coupling overvoltage peak is 17.08% higher than that of single pulse; the corona effect suppresses the peak overvoltage of transmission line under multi-pulse action by 7.29%; the peak value of overvoltage coupled with the phase conductor far from the lightning point is 17.5% different from the overvoltage of the phase conductor nearest to the lightning point. The conclusions of this paper can provide more accurate theoretical support for differential lightning protection design of transmission lines.