In recent years elephant flows are increasing by expansion of peer-to-peer (P2P) applications on the Internet. As a result, bandwidth is occupied by specific users triggering unfair resource allocation. The main packet-scheduling mechanism currently employed is first-in first-out (FIFO) where the available bandwidth of short flows is limited by elephant flows. Least attained service (LAS), which decides transfer priority of packets by the total amount of transferred data in all flows, was proposed to solve this problem. However, routers with LAS limit flows with large amount of transferred data even if they are low-rate. Therefore, it is necessary to improve the quality of low-rate flows with long holding times such as voice over Internet protocol (VoIP) applications. This paper proposes rate-based priority control (RBPC), which calculates the flow rate and control the priority by using it. Our proposed method can transfer short flows and low-rate flows in advance. Moreover, its fair performance is shown through simulations.