In practical exploration, the complex and diverse topographic effects are important for the processing and interpretation of EM exploration data. The interpretation of the electromagnetic data results in large errors when the influence of topographical factors is simply ignored. At present, the study of TEM is mainly based on the ideal situation of flat terrain, and the study of topographic effect is less. However, topographic relief is inevitable in practical exploration. In the paper, the correctness of the time-domain three-dimensional forward evolution based on the finite element method is verified by comparing the numerical results with those of the homogeneous full-space and half-space analytical solutions and the lumped high conductor model. In this paper, three-dimensional numerical simulations of time-domain transient electromagnetic methods are calculated based on the finite element method. Several exploration scenarios for complex terrain were constructed under the transmitting loop source, and the effect of terrain size and filling medium changes on the electromagnetic response was analyzed. The parameters of topographic effect, earth resistivity, surface resistivity and target conductivity are analyzed from z-component of magnetic field, apparent resistivity and time domain numerical solution, and the relative error distribution results in the whole observation period are shown. The results show that the influence of topographic effects on the electromagnetic response is concentrated in the early part of the time domain, with puddles of the same size having a higher influence on the electromagnetic response than raised soils and hollows. In practical exploration, puddles should be avoided where possible, while small sized topographic relief and hollows have a negligible effect on the electromagnetic response.