Graph convolutional networks (GCNs) have been widely used to process graph-structured data. However, existing GNN methods do not explicitly extract critical structures, which reflect the intrinsic property of a graph. In this work, we propose a novel GCN module named Neighbor Combinatorial ATtention (NCAT) to find critical structure in graph-structured data. NCAT attempts to match combinatorial neighbors with learnable patterns and assigns different weights to each combination based on the matching degree between the patterns and combinations. By stacking several NCAT modules, we can extract hierarchical structures that is helpful for down-stream tasks. Our experimental results show that NCAT achieves state-of-the-art performance on several benchmark graph classification datasets. In addition, we interpret what kind of features our model learned by visualizing the extracted critical structures.