The accurate identification of focal liver lesions (FLLs) is essential for liver diagnostics, with multimodal magnetic resonance imaging (MRI) providing comprehensive data pivotal for distinguishing liver tumors. In this paper, we introduce a modality-aware graph reasoning network for the classification of FLLs in multimodal MRI. Our model employs a shared-weight encoder for feature extraction and then constructs a fully connected graph. The graph uses modal features as the node embeddings and differentiable edge embedding mechanism to model the relationships between modalities. Subsequently, iterative message passing within the network refines node features by integrating complementary information from connected nodes. The effectiveness of our proposed method was evaluated on the LLD-MMRI2023 dataset and demonstrated better performance over conventional approaches.