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Graph Neural Networks (GNNs) have shown great ability in modeling graph-structured data for various domains. However, GNNs are known as black-box models that lack interpretability. Without understanding their inner working, we cannot fully trust them, which largely limits their adoption in high-stake scenarios. Though some initial efforts have been taken to interpret the predictions of GNNs, they mainly focus on providing post-hoc explanations using an additional explainer, which could misrepresent the true inner working mechanism of the target GNN. The works on self-explainable GNNs are rather limited. Therefore, we study a novel problem of learning prototype-based self-explainable GNNs that can simultaneously give accurate predictions and prototype-based explanations on predictions. We design a framework which can learn prototype graphs that capture representative patterns of each class as class-level explanations. The learned prototypes are also used to simultaneously make prediction for for a test instance and provide instance-level explanation. Extensive experiments on real-world and synthetic datasets show the effectiveness of the proposed framework for both prediction accuracy and explanation quality.