The overvoltage associated with direct lightning hits has been the important factor for the insulation design of a distribution line. In this paper, the sparkover rate of a medium-voltage line associated with direct lightning hits is investigated based on numerical calculations obtained by using EMTP and statistical analysis by taking account of the correlation between the peak value and the front duration of return-stroke current waveform. When the line is equipped with surge arresters at the interval of 100m in addition to the overhead ground wire, the sparkover rate associated with subsequent strokes is higher than that associated with first strokes. This demonstrates the importance of the study of current parameters for subsequent strokes.