Fog computing is a new computing paradigm that employs computation and network resources at the edge of a network to build small clouds, which perform as small data centers. In fog computing, lightweight virtualization (e.g., containers) has been widely used to achieve low overhead for performance-limited fog devices such as WiFi access points (APs) and set-top boxes. Unfortunately, containers have a weakness in the control of network bandwidth for outbound traffic, which poses a challenge to fog computing. Existing solutions for containers fail to achieve desirable network bandwidth control, which causes bandwidth-sensitive applications to suffer unacceptable network performance. In this paper, we propose qCon, which is a QoS-aware network resource management framework for containers to limit the rate of outbound traffic in fog computing. qCon aims to provide both proportional share scheduling and bandwidth shaping to satisfy various performance demands from containers while implementing a lightweight framework. For this purpose, qCon supports the following three scheduling policies that can be applied to containers simultaneously: proportional share scheduling, minimum bandwidth reservation, and maximum bandwidth limitation. For a lightweight implementation, qCon develops its own scheduling framework on the Linux bridge by interposing qCon’s scheduling interface on the frame processing function of the bridge. To show qCon’s effectiveness in a real fog computing environment, we implement qCon in a Docker container infrastructure on a performance-limited fog device—a Raspberry Pi 3 Model B board.