The task of multi-modal emotion recognition in conversation (MERC) aims to analyze the genuine emotional state of each utterance based on the multi-modal information in the conversation, which is crucial for conversation understanding. Existing methods focus on using graph neural networks (GNN) to model conversational relationships and capture contextual latent semantic relationships. However, due to the complexity of GNN, existing methods cannot efficiently capture the potential dependencies between long-distance utterances, which limits the performance of MERC. In this paper, we propose an Efficient Long-distance Latent Relation-aware Graph Neural Network (ELR-GNN) for multi-modal emotion recognition in conversations. Specifically, we first use pre-extracted text, video and audio features as input to Bi-LSTM to capture contextual semantic information and obtain low-level utterance features. Then, we use low-level utterance features to construct a conversational emotion interaction graph. To efficiently capture the potential dependencies between long-distance utterances, we use the dilated generalized forward push algorithm to precompute the emotional propagation between global utterances and design an emotional relation-aware operator to capture the potential semantic associations between different utterances. Furthermore, we combine early fusion and adaptive late fusion mechanisms to fuse latent dependency information between speaker relationship information and context. Finally, we obtain high-level discourse features and feed them into MLP for emotion prediction. Extensive experimental results show that ELR-GNN achieves state-of-the-art performance on the benchmark datasets IEMOCAP and MELD, with running times reduced by 52\% and 35\%, respectively.