Background: Code summarization automatically generates the corresponding natural language descriptions according to the input code. Comprehensiveness of code representation is critical to code summarization task. However, most existing approaches typically use coarse-grained fusion methods to integrate multi-modal features. They generally represent different modalities of a piece of code, such as an Abstract Syntax Tree (AST) and a token sequence, as two embeddings and then fuse the two ones at the AST/code levels. Such a coarse integration makes it difficult to learn the correlations between fine-grained code elements across modalities effectively. Aims: This study intends to improve the model's prediction performance for high-quality code summarization by accurately aligning and fully fusing semantic and syntactic structure information of source code at node/token levels. Method: This paper proposes a Multi-Modal Fine-grained Feature Fusion approach (MMF3) for neural code summarization. We introduce a novel fine-grained fusion method, which allows fine-grained fusion of multiple code modalities at the token and node levels. Specifically, we use this method to fuse information from both token and AST modalities and apply the fused features to code summarization. Results: We conduct experiments on one Java and one Python datasets, and evaluate generated summaries using four metrics. The results show that: 1) the performance of our model outperforms the current state-of-the-art models, and 2) the ablation experiments show that our proposed fine-grained fusion method can effectively improve the accuracy of generated summaries. Conclusion: MMF3 can mine the relationships between crossmodal elements and perform accurate fine-grained element-level alignment fusion accordingly. As a result, more clues can be provided to improve the accuracy of the generated code summaries.