Graph convolutional networks (GCNs) have been widely studied to address graph data representation and learning. In contrast to traditional convolutional neural networks (CNNs) that employ many various (spatial) convolution filters to obtain rich feature descriptors to encode complex patterns of image data, GCNs, however, are defined on the input observed graph G(X,A) and usually adopt the single fixed spatial convolution filter for graph data feature extraction. This limits the capacity of the existing GCNs to encode the complex patterns of graph data. To overcome this issue, inspired by depthwise separable convolution and DropEdge operation, we first propose to generate various graph convolution filters by randomly dropping out some edges from the input graph A . Then, we propose a novel graph-dropping convolution layer (GDCLayer) to produce rich feature descriptors for graph data. Using GDCLayer, we finally design a new end-to-end network architecture, that is, a graph-dropping convolutional network (GDCNet), for graph data learning. Experiments on several datasets demonstrate the effectiveness of the proposed GDCNet.