Recent automatic storytelling methods mainly rely on keyword planning or plot skeleton generation to model long-range dependencies and create consistent narrative texts. However, these approaches generate story plans or plots sequentially, leaving the non-sequential conception and structural design processes of human writers unexplored. To mimic human writers and exploit the fine-grained, intrinsic structural information of each story, we decompose automatic story generation into sub-problems of graph construction, graph generation, and graph-infused sequence generation. Specifically, we propose a graph-infused dual conditional variational autoencoder model to capture multi-level intra-story structures (i.e., graph) by continuous variational latent variables and generate consistent stories through dual-infusion of story structure planning and content learning. Experimental results on the ROCStories dataset and the CMU Movie Summary corpus confirm that our proposed model outperforms strong baselines in both human judges and widely-used automatic metrics.