Network embedding aims to represent a network into a low dimensional space where the network structural information and inherent properties are maximumly preserved. Random walk based network embedding methods such as DeepWalk and node2vec have shown outstanding performance in the aspect of preserving the network topological structure. However, these approaches either predict the distribution of a node's neighbors in both direction together, which makes them unable to capture any asymmetric relationship in a network; or preserve asymmetric relationship in only one direction and hence lose the one in another direction. To address these limitations, we propose bidirectional group random walk based network embedding method (BiGRW), which treats the distributions of a node's neighbors in the forward and backward direction in random walks as two different asymmetric network structural information. The basic idea of BiGRW is to learn a representation for each node that is useful to predict its distribution of neighbors in the forward and backward direction separately. Apart from that, a novel random walk sampling strategy is proposed with a parameter α to flexibly control the trade-off between breadth-first sampling (BFS) and depth-first sampling (DFS). To learn representations from node attributes, we design an attributed version of BiGRW (BiGRW-AT). Experimental results on several benchmark datasets demonstrate that the proposed methods significantly outperform the state-of-the-art plain and attributed network embedding methods on tasks of node classification and clustering.