In this study, a recently developed time-domain electromagnetic method called the short-offset grounded-wire transient electromagnetic (SOTEM) method, which is a near-source observation method, was adopted to obtain strong signals and great detection depths. The responses of the SOTEM and long-offset transient electromagnetic (LOTEM) methods were compared to further guide and promote the SOTEM method. Currently, the comparison between SOTEM and LOTEM methods is primarily based on one-dimensional (1D) models. However, most geological bodies are three-dimensional (3D) structures. We investigated the responses of a grounded-wire transient electromagnetic method based on 3D models using the 3D finite-difference time-domain method. In addition, the signal strengths, detection sensitivities and detection depths of the SOTEM and LOTEM methods were compared. The results revealed that the field amplitudes of Ex (electrical component parallel to the transmitting source) and ∂By/∂t (magnetic component perpendicular to the transmitting source horizontally) were higher at the short offsets than at the long offsets. For the ∂Bx/∂t (magnetic component parallel to the transmitting source) and the vertical magnetic component ∂Bz/∂t, at initial times, the responses received would be stronger when closer to the transmitting source, whereas at later times, the responses would be stronger when farther from the source. Ex detection sensitivity increased with an increase in the offset at initial times, and increased with a decrease in the offset at later times. The detection sensitivities of the three magnetic field components at short offsets were higher than those at long offsets. The ∂By/∂t effective detection depth was the greatest. Generally, the effective detection depths of the three magnetic field components increased with decreasing offset. The range of the ratio of the horizontal distance, r, between the transmitting source and the target body to the effective detection depth H was 0.5-1.1.