Hyperbolic space is a well-defined space with constant negative curvature. Recent research demonstrates its odds of capturing complex hierarchical structures with its exceptional high capacity and continuous tree-like properties. This paper bridges hyperbolic space's superiority to the power-law structure of documents by introducing a hyperbolic neural network architecture named Hyperbolic Hierarchical Attention Network (Hype-HAN). Hype-HAN defines three levels of embeddings (word/sentence/document) and two layers of hyperbolic attention mechanism (word-to-sentence/sentence-to-document) on Riemannian geometries of the Lorentz model, Klein model and Poincaré model. Situated on the evolving embedding spaces, we utilize both conventional GRUs (Gated Recurrent Units) and hyperbolic GRUs with Möbius operations. Hype-HAN is applied to large scale datasets. The empirical experiments show the effectiveness of our method.