Multimodal Emotion Recognition in Conversation (MERC) aims to recognize emotions in conversational videos by fusing multimodal information. Current methods mainly rely on the direct fusion of emotional representations. This simple concatenation or linear combination not only fails to fully explore the deep semantic correlations and cross-modal dependencies among visual, textual, audio and other modalities, but also causes redundant feature interference due to the heterogeneity and misalignment of features from different modalities. Therefore, this paper proposes the Graph Dynamic Fusion Network with Modality Mutual Information Maximization (MMGDFN), designed to effectively exploit the complementarity among modalities in conversations. Specifically, by constructing dynamic graph networks to model the interaction relationships among features of various modalities, the method adaptively captures cross-modal dependencies through graph structures. Meanwhile, a mutual information maximization mechanism is introduced to quantify and enhance complementary information among modalities, enabling adaptive balancing of multimodal complementary information and effective filtering of redundant features. Experimental results on two publicly available datasets (i.e. IEMOCAP and MELD) demonstrate that the proposed MMGDFN significantly outperforms state-of-the-art multimodal emotion recognition methods.