In this paper, we propose multi-layer non-negative matrix factorization (NMF) network for classification task, which provides intuitively understandable hierarchical feature learning process. The layer-by-layer learning strategy was adopted through stacked NMF layers, which enforced non-negativity of both features and their coefficients. With the non-negativity constraint, the learning process revealed latent feature hierarchies in the complex data in intuitively understandable manner. The multi-layer NMF networks was investigated for classification task by studying various network architectures and nonlinear functions. The proposed multilayer NMF network was applied to document classification task, and demonstrated that our proposed multi-layer NMF network resulted in much better classification performance compared to single-layered network, even with the small number of features. Also, through intuitive learning process, the underlying structure of feature hierarchies was revealed for the complex document data.