Graft-versus-host disease (GVHD) is a rare but often fatal complication in liver transplantation, with a very high mortality rate. By harnessing multi-modal deep learning methods to integrate heterogeneous and imbalanced electronic health records (EHR), we aim to advance early prediction of GVHD, paving the way for timely intervention and improved patient outcomes. In this study, we analyzed pre-transplant electronic health records (EHR) spanning the period before surgery for 2,100 liver transplantation patients, including 42 cases of graft-versus-host disease (GVHD), from a cohort treated at Mayo Clinic between 1992 and 2025. The dataset comprised four major modalities: patient demographics, laboratory tests, diagnoses, and medications. We developed a multi-modal deep learning framework that dynamically fuses these modalities, handles irregular records with missing values, and addresses extreme class imbalance through AUC-based optimization. The developed framework outperforms all single-modal and multi-modal machine learning baselines, achieving an AUC of 0.836, an AUPRC of 0.157, a recall of 0.768, and a specificity of 0.803. It also demonstrates the effectiveness of our approach in capturing complementary information from different modalities, leading to improved performance. Our multi-modal deep learning framework substantially improves existing approaches for early GVHD prediction. By effectively addressing the challenges of heterogeneity and extreme class imbalance in real-world EHR, it achieves accurate early prediction. Our proposed multi-modal deep learning method demonstrates promising results for early prediction of a GVHD in liver transplantation, despite the challenge of extremely imbalanced EHR data.