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Graph Convolutional Network (GCN) has exhibited strong empirical performance in many real-world applications. The vast majority of existing works on GCN primarily focus on the accuracy while ignoring how confident or uncertain a GCN is with respect to its predictions. Despite being a cornerstone of trustworthy graph mining, uncertainty quantification on GCN has not been well studied and the scarce existing efforts either fail to provide deterministic quantification or have to change the training procedure of GCN by introducing additional parameters or architectures. In this paper, we propose the first frequentist-based approach named JuryGCN in quantifying the uncertainty of GCN, where the key idea is to quantify the uncertainty of a node as the width of confidence interval by a jackknife estimator. Moreover, we leverage the influence functions to estimate the change in GCN parameters without re-training to scale up the computation. The proposed JuryGCN is capable of quantifying uncertainty deterministically without modifying the GCN architecture or introducing additional parameters. We perform extensive experimental evaluation on real-world datasets in the tasks of both active learning and semi-supervised node classification, which demonstrate the efficacy of the proposed method.