Graph convolutional networks (GCNs) have achieved great success on graph-structured data. Many GCNs can be considered low-pass filters for graph signals. In this paper, we propose a more powerful GCN, named BiGCN, that extends to bidirectional filtering. Specifically, we consider the original graph structure information and the latent correlation between features. Thus BiGCN can filter the signals along with both the original graph and a latent feature-connection graph. Compared with most existing GCNs, BiGCN is more robust and has powerful capacities for feature denoising. We perform node classification and link prediction in citation networks and co-purchase networks with three settings: Noise-Rate, Noise-Level, and Structure-Mistakes. Extensive experimental results demonstrate that our model outperforms the state-of-the-art graph neural networks in both clean and artificially noisy data.