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In recent years, analyzing the explanation for the prediction of Graph Neural Networks (GNNs) has attracted increasing attention. Despite this progress, most existing methods do not adequately consider the inherent uncertainties stemming from the randomness of model parameters and graph data, which may lead to overconfidence and misguiding explanations. However, it is challenging for most of GNN explanation methods to quantify these uncertainties since they obtain the prediction explanation in apost-hocand model-agnostic manner without considering the randomness ofgraph dataandmodel parameters. To address the above problems, this paper proposes a novel uncertainty quantification framework for GNN explanations. For mitigating the randomness of graph data in the explanation, our framework accounts for two distinct data uncertainties, allowing for a direct assessment of the uncertainty in GNN explanations. For mitigating the randomness of learned model parameters, our method learns the parameter distribution directly from the data, obviating the need for assumptions about specific distributions. Moreover, the explanation uncertainty within model parameters is also quantified based on the learned parameter distributions. This holistic approach can integrate with anypost-hocGNN explanation methods. Empirical results from our study show that our proposed method sets a new standard for GNN explanation performance across diverse real-world graph benchmarks.