With its characteristics of decentralization, security, data traceability, and tamper-resistance, the blockchain has been widely used in various domains. Considering the difference in the performance of the devices, the light client is proposed so that devices without the ability to store a full blockchain copy can also participate in the blockchain transactions. However, the light client has to communicate with full nodes and verify the authenticity of a transaction which brings in some extent of communication, computation, and storage overheads to the light client. These overheads cannot be ignored for some low-performance devices, such as embedded devices or IoT chips, and therefore the current light client scheme does not work in this situation. We propose LOPE (a Low-overhead payment vErification method) for poor-capacity nodes in the blockchain system. In LOPE, a grouping protocol is designed to partition full nodes into groups to serve the verification requests of the light client. In addition, Practical byzantine fault tolerance (PBFT) is used to ensure the light client to get a credible result in spite of a few dishonest nodes existing in the group. We conduct LOPE and evaluate it in a testbed. The experiment results show that LOPE reduces more than half of the communication overhead, degrades the computation overhead of the light client to a large extent, and avoids the storage overhead of the hash roots of block headers in the light client. We also conduct theoretical analysis to show the performance improvement and security issues of LOPE.