Recently cloud-based graph convolutional network (GCN) has demonstrated great success and potential in many privacy-sensitive applications such as personal healthcare and financial systems. Despite its high inference accuracy and performance on cloud, maintaining data privacy in GCN inference, which is of paramount importance to these practical applications, remains largely unexplored. In this paper, we take an initial attempt towards this and develop $\textit{CryptoGCN}$--a homomorphic encryption (HE) based GCN inference framework. A key to the success of our approach is to reduce the tremendous computational overhead for HE operations, which can be orders of magnitude higher than its counterparts in the plaintext space. To this end, we develop an approach that can effectively take advantage of the sparsity of matrix operations in GCN inference to significantly reduce the computational overhead. Specifically, we propose a novel AMA data formatting method and associated spatial convolution methods, which can exploit the complex graph structure and perform efficient matrix-matrix multiplication in HE computation and thus greatly reduce the HE operations. We also develop a co-optimization framework that can explore the trade offs among the accuracy, security level, and computational overhead by judicious pruning and polynomial approximation of activation module in GCNs. Based on the NTU-XVIEW skeleton joint dataset, i.e., the largest dataset evaluated homomorphically by far as we are aware of, our experimental results demonstrate that $\textit{CryptoGCN}$ outperforms state-of-the-art solutions in terms of the latency and number of homomorphic operations, i.e., achieving as much as a 3.10$\times$ speedup on latency and reduces the total Homomorphic Operation Count by 77.4\% with a small accuracy loss of 1-1.5$\%$.