Despite recent progress in Graph Neural Networks (GNNs), explaining predictions made by GNNs remains a challenging open problem. The leading method mainly addresses the local explanations (i.e., important subgraph structure and node features) to interpret why a GNN model makes the prediction for a single instance, e.g. a node or a graph. As a result, the explanation generated is painstakingly customized for each instance. The unique explanation interpreting each instance independently is not sufficient to provide a global understanding of the learned GNN model, leading to the lack of generalizability and hindering it from being used in the inductive setting. Besides, as it is designed for explaining a single instance, it is challenging to explain a set of instances naturally (e.g., graphs of a given class). In this study, we address these key challenges and propose PGExplainer, a parameterized explainer for GNNs. PGExplainer adopts a deep neural network to parameterize the generation process of explanations, which enables PGExplainer a natural approach to multi-instance explanations. Compared to the existing work, PGExplainer has a better generalization power and can be utilized in an inductive setting easily. Experiments on both synthetic and real-life datasets show highly competitive performance with up to 24.7\% relative improvement in AUC on explaining graph classification over the leading baseline.