A transient response of a cable with a two-layer conductor, such as a conductor including a semiconductive layer, is analyzed by means of a finite-difference time-domain (FDTD) method. Prior to this analysis, the accuracy of a transient analysis by this method, is investigated in comparison with an EMTP simulation for a single-core cable without a two-layer conductor. Current waveforms at the sending and receiving ends of the cable, calculated by FDTD method, agree well with those calculated by EMTP. In the case of a simulation for the cable including a semiconductive layer which is the second layer of a two-layer conductor, current waveforms at the both ends of the cable are distorted depending on the conductivity of the second layer. Also, the propagation velocity of a surge current is dependent on it. When the conductivity of the second layer ranges from 0.001 to 0.1 S/m, the shunt admittance of the cable dominates the above phenomena. On the other hand, they are ascribable to the series impedance when the conductivity is higher.