Random walks are widely adopted in various network analysis tasks ranging from network embedding to label propagation. It could capture and convert geometric structures into structured sequences while alleviating the issues of sparsity and curse of dimensionality. Though random walks on plain networks have been intensively studied, in real-world systems, nodes are often not pure vertices, but own different characteristics, described by the rich set of data associated with them. These node attributes contain plentiful information that often complements the network, and bring opportunities to the random-walk-based analysis. However, it is unclear how random walks could be developed for attributed networks towards an effective joint information extraction. Node attributes make the node interactions more complicated and are heterogeneous with respect to topological structures. To bridge the gap, we explore to perform joint random walks on attributed networks, and utilize them to boost the deep node representation learning. The proposed framework GraphRNA consists of two major components, i.e., a collaborative walking mechanism - AttriWalk, and a tailored deep embedding architecture for random walks, named graph recurrent networks (GRN). AttriWalk considers node attributes as a bipartite network and uses it to propel the walking more diverse and mitigate the tendency of converging to nodes with high centralities. AttriWalk enables us to advance the prominent deep network embedding model, graph convolutional networks, towards a more effective architecture - GRN. GRN empowers node representations to interact in the same way as nodes interact in the original attributed network. Experimental results on real-world datasets demonstrate the effectiveness of GraphRNA compared with the state-of-the-art embedding algorithms.