Recent years have witnessed growing interests in multimedia recommendation, which aims to predict whether a user will interact with an item with multimodal contents. Previous studies focus on modeling user-item interactions with multimodal features included as side information. However, this scheme is not well-designed for multimedia recommendation. Firstly, only collaborative item-item relationships are implicitly modeled through high-order item-user-item co-occurrences. We argue that the latent semantic item-item structures underlying these multimodal contents could be beneficial for learning better item representations and assist the recommender models to comprehensively discover candidate items. Secondly, previous studies disregard the fine-grained multimodal fusion. Although having access to multiple modalities might allow us to capture rich information, we argue that the simple coarse-grained fusion by linear combination or concatenation in previous work is insufficient to fully understand content information and item relationships.To this end, we propose a latent structure MIning with ContRastive mOdality fusion method (MICRO for brevity). To be specific, we devise a novel modality-aware structure learning module, which learns item-item relationships for each modality. Based on the learned modality-aware latent item relationships, we perform graph convolutions that explicitly inject item affinities to modality-aware item representations. Then, we design a novel contrastive method to fuse multimodal features. These enriched item representations can be plugged into existing collaborative filtering methods to make more accurate recommendations. Extensive experiments on real-world datasets demonstrate the superiority of our method over state-of-the-art baselines.