With the deep integration of the travel and energy industries, cross-industry supply chain finance has gradually become a high-risk field of hidden money laundering incidents. For this reason, this work proposes a graph-driven cross-industry real-time anti-money laundering monitoring framework (GCRMF) for integrated travel - energy supply chain networks. First, a cross-industry heterogeneous graph (CIHG) covering new energy vehicle rental platforms, energy suppliers, fintech institutions, etc., is constructed, and industry semantics are integrated through temporarily Dual-GAT (Temporal Dual-Graph Attention Network), dynamically encoding capital flow paths and evolution features over time. Subsequently, in order to identify the structural fraud behavior together produced by colluding subjects, a meta-path subgraph reasoning module based on contrastive learning and hierarchical graph sampling is proposed to enhance the discrimination capability of cross-industry recurring money laundering behavior. Meanwhile, a self-supervised online learning mechanism is adopted for real-time adaptation and continuous optimization to new money laundering strategies. The experimental results show that compared with existing graph neural network methods in cross-industry scenarios, GCRMF improves the performance by more than 17.8% of F1 score and greatly reduces the false positive rate.