A time-domain electric field integral equation of a thin wire conductor is built, and the transient current induced on the wire and the transient electric fields are calculated by the time domain moment of method combined with the marching on in time procedure (MOT). Meanwhile, the transient responses of thin wire above real ground with different conductivity are computed, and the effect of the ground is discussed. The precision and computation time of the method is compared with the commercial software CDEGS.