Graphs are ubiquitous across the globe and within science and engineering. With graphs growing in size, node classification on large graphs can be space and time consuming, even with powerful classifiers such as Graph Convolutional Networks (GCNs). Hence, some questions are raised, particularly, whether one can keep only some of the edges of a graph while maintaining prediction performance for node classification, or train classifiers on specific subgraphs instead of a whole graph with limited performance loss in node classification. To address these questions, we propose Sparsified Graph Convolutional Network (SGCN), a neural network graph sparsifier that sparsifies a graph by pruning some edges. We formulate sparsification as an optimization problem, which we solve by an Alternating Direction Method of Multipliers (ADMM)-based solution. We show that sparsified graphs provided by SGCN can be used as inputs to GCN, leading to better or comparable node classification performance with that of original graphs in GCN, DeepWalk, and GraphSAGE.