The semi-airborne transient electromagnetic method using short-offset has the characteristics of high signal-to-noise ratio and large detection depth, which can adapt to environmental monitoring, groundwater mapping and metal survey in complex terrain. The terrain effects will modulate semi-airborne transient electromagnetic method response. Most terrains effects studies assume that the anomalous body is located below the centre of topography or under the slope, however, in the direction of electromagnetic propagation, several scenarios exist regarding the position of an anomalous body relative to a topography, and different situations will have different anomalous characteristics. In this study, the time-domain finite-element modelling using unstructured mesh is used to investigate the distribution of the electromagnetic response of different time channels of different anomalous bodies in different positions relative to a topography under two conditions: mountains and valleys. The results show that (1) The influence of the relative position of the anomalous body and the topography is similar in the mountain and valley. When the anomalous body is located on the side of the topography far from the transmitter, it is more affected by the topography than when the anomalous body is located on the side of the topography near the transmitter, and (2) in the early stage, the distribution of the electromagnetic response is primarily determined by the topography, in the middle stage, the coupling between anomalous bodies at different locations and the topography results in an extremely complex response distribution, in the late stage, the response distribution primarily originates from the eddy current of the anomalous body, and the effect of the topography is moderate. When using semi-airborne transient electromagnetic method for environmental monitoring and shallow resources survey in complex terrain, data processing and interpretation should be performed based on the position of the anomalous body relative to the topography.