The advent of software-defined networking (SDN) has led to the paradigm of programmable network environments. Conceptually, the structure of SDN is divided into three layers: application, control, and infrastructure. The SDN controller in the control layer can configure and execute the routing of applications to the infrastructure layer consisting of network devices, including hosts and switches. Current studies on SDN have predominantly focused on control layer aspects, such as controller development, performance aspects of the controller, and interaction among different controllers and between controllers and network devices. However, to provide seamless network services and efficiently manage network environments, application-aware routing is essential because applications may have different quality of service (QoS) requirements, such as maximum bandwidth and minimum delay. This study proposes the Network Situation-Aware Framework (NSAF) to more efficiently handle application routing based on the QoS requirements and changing network status. A mechanism for supporting the NSAF consisting of application registration, network status monitoring, violation detection, and routing control is also presented. The applicability and feasibility of the proposed NSAF are verified by implementing a prototype. The NSAF may be used as a reference model for efficiently managing SDN-based networks to ensure application QoS.