Word-character lattice models have been proved to be effective for Chinese named entity recognition (NER), in which word boundary information is fused into character sequences for enhancing character representations. However, prior approaches have only used simple methods such as feature concatenation or position encoding to integrate word-character lattice information, but fail to capture fine-grained correlations in word-character spaces. In this paper, we propose DCSAN, a Dynamic Cross- and Self-lattice Attention Network that aims to model dense interactions over word-character lattice structure for Chinese NER. By carefully combining cross-lattice and self-lattice attention modules with gated word-character semantic fusion unit, the network can explicitly capture fine-grained correlations across different spaces (e.g., word-to-character and character-to-character), thus significantly improving model performance. Experiments on four Chinese NER datasets show that DCSAN obtains stateof-the-art results as well as efficiency compared to several competitive approaches.