In Wireless Sensor Networks (WSNs), Energy Harvesting (EH) is emerging as a promising solution to realize the energy-efficient green communications. Non-EH nodes can save the energy by using EH nodes as relaying nodes, and relaying with the better throughput is required to efficiently consume the precious energy. In most cases, the EH charging rate gets low since current charging techniques cannot convert the environmental energy well, so it is important to achieve high performance in low charging rate. In this paper, we propose an adaptive relay selection scheme based on the average charging rate to achieve better throughput even in low charging rate. In our scheme, each node adaptively changes the criterion to be a relaying candidate based on the current charging rate; an EH node whose charging rate is low raises the threshold to save the precious energy for better channel condition. By the computer simulation, we show that our proposed relay selection scheme achieves the better throughput than that of the conventional schemes in low charging rate, which is the more realistic condition.