Transient electromagnetic method, in the area of poor terrain conditions, the transient electromagnetic prospecting method is often not good, the reason: ignore the influence of the terrain factors, resulting in a larger deviation of interpretation results . In this paper, by using the finite difference time domain method to simulate the terrain of transient electromagnetic response, The transient electromagnetic diffusion equation is derived directly from the Maxwell equation, and the finite difference time domain finite difference equation is constructed by introducing the virtual displacement current. First, the analytical model of homogeneous half space solutions were compared with the results of the calculation, test the algorithm accuracy; then, Simulation analysis of the peaks and valley terrain model response characteristics, It?concluded?that the early signal performance for two kinds of features, the front valley terrain, earlier than normal terrain induced electromotive force value decreased, resulting in false high resistivity anomaly, early after than the normal terrain induced electromotive force value increased, resulting in false low resistivity anomalies, mountain terrain features on the contrary, late signal terrain effect gradually weakened; finally, the measured data prove the correctness of this simulation results. The research results have good reference significance for terrain effect recognition and correction.