Handover support is one of the important issues in mobile networks to guarantee the quality of service (QoS) requirements for mobile users. Alongside the development of network technologies, handover management to provide service continuity has been researched and applied for the Internet or cellular networks such as 3G/4G/5G. However, each network paradigm provides its own individual handover management system, even though there are different kinds of QoS requirements for various mobile services. This causes inefficient network resource utilization from the network operators’ perspectives. Therefore, this paper proposes a QoS-aware flexible mobility management scheme for software-defined networking (SDN)-based mobile networks. The proposed scheme classifies flows into four classes based on the QoS requirements of services in terms of delay and loss tolerance. According to the classified service characteristics, it provides a differential handover method for each flow class to support efficient network operation without any service degradation by interacting between the forwarding plane nodes and SDN controller. The performance analysis shows that the proposed scheme enables flexible network resource utilization, satisfying the QoS requirements for each class well compared to the conventional schemes that only consider their own individual handover procedure.