Graph Neural Networks (GNNs) have emerged as powerful tools for analyzing and learning representations from graph-structured data. A crucial prerequisite for the outstanding performance of GNNs is the availability of complete graph information, i.e., node features and graph structure, which is frequently unmet in real-world scenarios since graphs are often incomplete due to various uncontrollable factors. Existing approaches only focus on dealing with either incomplete features or incomplete structure, which leads to performance loss inevitably. To address this issue, this study proposes a mutual dual-stream graph neural network (MDS-GNN), which implements a mutual benefit learning between features and structure. Its main ideas are as follows: a) reconstructing the missing node features based on the initial incomplete graph structure; b) generating an augmented global graph based on the reconstructed node features, and propagating the incomplete node features on this global graph; and c) utilizing contrastive learning to make the dual-stream process mutually benefit from each other. Extensive experiments on six real-world datasets demonstrate the effectiveness of our proposed MDS-GNN on incomplete graphs.