For IP-based mobile networks, efficient mobility management is vital to provision seamless online service. IP address starvation and scalability issue constrain the wide deployment of existing mobility schemes, such as Mobile IP, Proxy Mobile IP, and their derivations. Most of the studies focus on the scenario of mobility among public networks. However, most of current networks, such as home networks, sensor networks, and enterprise networks, are deployed with private networks hard to apply mobility solutions. With the rapid development, Software Defined Networking (SDN) offers the opportunity of innovation to support mobility in private network schemes. In this paper, a novel mobility management scheme is presented to support mobile node moving from public network to private network in a seamless handover procedure. The centralized control manner and flexible flow management in SDN are utilized to provide network-based mobility support with better QoS guarantee. Benefiting from SDN/OpenFlow technology, complex handover process is simplified with fewer message exchanges. Furthermore, handover efficiency can be improved in terms of delay and overhead reduction, scalability, and security. Analytical analysis and implementation results showed a better performance than mobile IP in terms of latency and throughput variation.