Building on top of blockchain, payment channel networks-backed (PCNs) cryptocurrencies emerge as a promising solution for a mobile payment system with fewer intermediaries, more security, higher speed, and lower cost. A key problem for PCN is payment channel rebalancing, that is, finding a set of circular transactions that restore a PCN with skewed channel balances back into an equilibrium state. However, existing practice on payment channel rebalancing either has a hard limit on the problem size or tends to fall into local optimum. To address these challenges, we propose DRL-PCR, a Deep Reinforcement Learning-based Payment Channel Rebalancing algorithm. On one hand, DRL-PCR leverages the strong approximation ability of deep neural networks to handle large problem spaces. On the other hand, DRL-PCR decomposes the rebalancing problem into a sequence of decision-making problems and progressively builds the final solution. By aiming to find a globally optimized solution and solving the long-term optimization model of DRL, DRL-PCR is superior to greedy-based algorithms and can mitigate the risk of getting trapped in a local optimum. In particular, payment channel rebalancing typically involves dealing with graph-structured data, where the major obstacle lies in understanding the sophisticated circular dependencies between payment channels and routing paths. DRL-PCR achieves this by encoding the input data with a novel graph neural network-based model and capturing the circular dependencies through a customized message passing process. In addition, considering the distributed nature of PCN, DRL-PCR uses a leadership election protocol to elect leaders for decision-making. Evaluations on the historical data of two real-world PCNs demonstrate that DRL-PCR can restore the PCN to a more balanced state and improve the transaction throughput and success ratios by up to 2.1x and 1.6x, respectively.