Graph neural networks (GNNs) have recently emerged as revolutionary technologies for machine learning tasks on graphs. In GNNs, the graph structure is generally incorporated with node representation via the message passing scheme, making the explanation much more challenging. Given a trained GNN model, a GNN explainer aims to identify a most influential subgraph to interpret the prediction of an instance (e.g., a node or a graph), which is essentially a combinatorial optimization problem over graph. The existing works solve this problem by continuous relaxation or search-based heuristics. But they suffer from key issues such as violation of message passing and hand-crafted heuristics, leading to inferior interpretability. To address these issues, we propose a RL-enhanced GNN explainer, RG-Explainer, which consists of three main components: starting point selection, iterative graph generation and stopping criteria learning. RG-Explainer could construct a connected explanatory subgraph by sequentially adding nodes from the boundary of the current generated graph, which is consistent with the message passing scheme. Further, we design an effective seed locator to select the starting point, and learn stopping criteria to generate superior explanations. Extensive experiments on both synthetic and real datasets show that RG-Explainer outperforms state-of-the-art GNN explainers. Moreover, RG-Explainer can be applied in the inductive setting, demonstrating its better generalization ability.