The relationships between objects in a network are typically diverse and complex, leading to the heterogeneous edges with different semantic information. In this paper, we focus on exploring the heterogeneous edges for network representation learning. By considering each relationship as a view that depicts a specific type of proximity between nodes, we propose a multi-stage non-negative matrix factorization (MNMF) model, committed to utilizing abundant information in multiple views to learn robust network representations. In fact, most existing network embedding methods are closely related to implicitly factorizing the complex proximity matrix. However, the approximation error is usually quite large, since a single low-rank matrix is insufficient to capture the original information. Through a multi-stage matrix factorization process motivated by gradient boosting, our MNMF model achieves lower approximation error. Meanwhile, the multi-stage structure of MNMF gives the feasibility of designing two kinds of non-negative matrix factorization (NMF) manners to preserve network information better. The united NMF aims to preserve the consensus information between different views, and the independent NMF aims to preserve unique information of each view. Concrete experimental results on realistic datasets indicate that our model outperforms three types of baselines in practical applications.