Knowledge of flow distributions from a stream of packets passing through a network link helps a network operator infer traffic demands, characterize source traffic, and detect traffic anomalies. Flow monitoring provides critical information for many network applications, and some approaches have been proposed to address flow monitoring. However, they either lack accuracy, or require intensive computing resources. In this paper, we propose a Resource-Efficient System (called RES) for monitoring flow distribution, which consists of Double sampling module, Online streaming module, and Offline processing module. Using real network traffic traces, we show that the RES indeed produces the desired accuracy in monitoring flow distribution.