BACKGROUND & AIMS: Microvascular invasion (MVI) is associated with poor prognosis in hepatocellular carcinoma (HCC). Topology may improve the predictive performance and interpretability of deep learning (DL). We aimed to develop and externally validate an MRI-based topology DL model for preoperative prediction of MVI. METHODS: This dual-centre retrospective study included consecutive surgically treated HCC patients from two tertiary care hospitals. Automatic liver and tumour segmentations were performed with DL methods. A pure convolutional neural network (CNN) model, a topology-CNN (TopoCNN) model and a topology-CNN-clinical (TopoCNN+Clinic) model were developed and externally validated. Model performance was assessed using the area under the receiver operating characteristic curve (AUC). Cox regression analyses were conducted to identify risk factors for recurrence-free survival within 2 years (early RFS) and overall survival (OS). RESULTS: In total, 589 patients were included (292 [49.6%] with pathologically confirmed MVI). The AUCs of the TopoCNN and TopoCNN+Clinic models were 0.890 and 0.895 for the internal test dataset and 0.871 and 0.879 for the external test dataset, respectively. For tumours ≤ 3.0 cm, the AUCs of the TopoCNN and TopoCNN+Clinic models were 0.879 and 0.929 for the internal test dataset, and 0.763 and 0.758 for the external test dataset. The TopoCNN-derived MVI prediction probability was an independent risk factor for early RFS (hazard ratio 6.64) and OS (hazard ratio 13.33). CONCLUSIONS: The MRI topological DL model based on automatic liver and tumour segmentation could accurately predict MVI and effectively stratify postoperative early RFS and OS, which may assist in personalised treatment decision-making.