Money laundering is an illicit activity that seeks to conceal the nature and origins of criminal proceeds, posing a substantial threat to the national economy, the political order, and social stability. To scientifically and reasonably predict money laundering risks, this paper focuses on the “layering” stage of the money laundering process in the field of supervised learning for money laundering fraud prediction. A money laundering and fraud prediction model based on deep learning, referred to as MDGC-LSTM, is proposed. The model combines the use of a dynamic graph convolutional network (MDGC) and a long short-term memory (LSTM) network to efficiently identify illegal money laundering activities within financial transactions. MDGC-LSTM constructs dynamic graph snapshots with symmetrical spatiotemporal structures based on transaction information, representing transaction nodes and currency flows as graph nodes and edges, respectively, and effectively captures the relationships between temporal and spatial structures, thus achieving the dynamic prediction of fraudulent transactions. The experimental results demonstrate that compared with traditional algorithms and other deep learning models, MDGC-LSTM achieves significant advantages in comprehensive spatiotemporal feature modeling. Specifically, based on the Elliptic dataset, MDGC-LSTM improves the Macro-F1 score by 0.25 compared to that of the anti-money laundering fraud prediction model currently considered optimal.