Multi-modal conversational emotion recognition aims to identify the emotions of speakers in continuous conversation with multi-modal data, w.r.t., textual (content), visual (face), and acoustic (speech) data. Mainstream graph-based methods capture only limited contextual information within the graph structure (local information) while neglecting long-distance critical context outside the graph (global information). We propose a Triple Context-Aware Network (TCAN) that fuses local speaker-specific utterance features, global long-distance key context, and global temporal features, which maximizes the capture of global contextual representations and local details. Therefore, TCAN successfully models context with high quality, better revealing the implicit emotional state within the dialogue. We conducted extensive comparative and multi-dimensional ablation experiments to validate the effectiveness of our method and proposed structure. The results prove that our approach outperforms competitors by 2.7% and exhibits strong robustness.