As one of the effective methods used in search for mineral resources, down-hole transient electromagnetic method (TEM) measures transient electromagnetic field in a drill hole by placing receiving coils in the drill hole. Based on time domain finite difference algorithm, the authors used loop source and non-uniform gird to simulate the response of the uniform medium in half space, inclined conductor, and inclined conductor with overburden. The results indicate that the maximum value of response decreases with delay time in uniform half space. When the source is laid on the receiving drill hole, the abnormal response is reflected apparently. When the source is laid beside the receiving drill hole, abnormal response can be observed with more observation time. The influence of overburden exists all over the observation time, which causes the decrease of the abnormal response. It is also weakened with the increasing distance between transmit loop and receiving drill hole. The research provides reference for analysis and interpretation of down-hole TEM abnormal response characteristics.