Utilizing neural network models to inverse time-domain electromagnetic signals enables rapid acquisition of electrical structures, a non-intrusive method widely applied in geological and environmental surveys. However, traditional multi-layer perceptron (MLP) feature extraction is limited, struggling with cases involving complex electrical media with induced polarization effects, thereby limiting the inversion model’s predictive capacity. A graph-topology-based neural network model for strata electrical structure imaging with long-dependency feature extraction was proposed. We employ graph convolutional networks (GCN) for capturing non-Euclidean features like resistivity-thickness coupling and Long Short-Term Memory (LSTM) to capture long-dependency features. The LSTM compensates for GCN’s constraints in capturing distant node relationships. Using case studies with 5-strata and 9-strata resistivity models containing induced polarization effects, compared to traditional MLP networks, the proposed model utilizing time-domain features and graph-topology-based electrical structure extraction significantly improves performance. The mean absolute error in inversion misfit is reduced from 10–20% to around 2–3%.