We propose a general strategy named ‘divide, conquer and combine’ for multimodal fusion. Instead of directly fusing features at holistic level, we conduct fusion hierarchically so that both local and global interactions are considered for a comprehensive interpretation of multimodal embeddings. In the ‘divide’ and ‘conquer’ stages, we conduct local fusion by exploring the interaction of a portion of the aligned feature vectors across various modalities lying within a sliding window, which ensures that each part of multimodal embeddings are explored sufficiently. On its basis, global fusion is conducted in the ‘combine’ stage to explore the interconnection across local interactions, via an Attentive Bi-directional Skip-connected LSTM that directly connects distant local interactions and integrates two levels of attention mechanism. In this way, local interactions can exchange information sufficiently and thus obtain an overall view of multimodal information. Our method achieves state-of-the-art performance on multimodal affective computing with higher efficiency.