The grounded-source transient electromagnetic (TEM) method, which enjoys the advantages of high topographic adaptability and large exploration depths, is suitable for deep resource exploration in mountainous areas. However, the TEM responses can be distorted due to topographic effects, causing great difficulties in data interpretation. This study investigated the influence patterns and correction method of topographic effects based on the three-dimensional unstructured time-domain finite element method. First, this study conducted the fine-scale description of mountains using unstructured tetrahedral grids, calculated the response of various topographic models, and analyzed the influence patterns of topographic effects. Then, it proposed a correction method for topographic effects based on the principle of the linear superposition principle of electromagnetic fields, established a geoelectric model of mountains according to the actual elevation data, and calculated the model responses through three-dimensional forward modeling. Subsequently, this study determined the topographic responses by subtracting the flat Earth model responses from the mountain model responses and then obtained the corrected TEM responses by removing the topographic responses from the total responses. The results are as follows: (1) The influence of mountains on the TEM responses is concentrated in the early stage and weakens gradually with time; (2) The topographic effects are concentrated near mountains, and their intensity depends on the distance of survey points from mountain peaks; (3) The influencing range and response amplitude of mountains are proportional to the mountain scale. In other words, a larger mountain scale corresponds to a larger influencing range and higher response amplitude; (4) Mountains with relatively high resistivity show more intense topographic influence. As shown by multiple models with simple and regular topographic anomalies, the corrected TEM responses, which match well with the responses from direct forward modeling, can effectively eliminate topographic effects to a certain extent. The research on the influence and correction method of topographic effects can be used as a reference for the processing and interpretation of TEM data of areas with complex terrain.