All active sessions of an ordinary host will be broken if the host changes its IP address as a result of migrating to a new subnet. Traditional solutions toward this problem either need modifying mobile hosts or create tunnels that cause inefficient triangle routing. SDN-based mobility schemes, on the other hand, focus on handover latency reduction or fast packet redirection after handover. There is no SDN-based approach that handles autonomous IP address changes by mobile hosts. As a remedy, we propose SDN-enabled Session Continuity (SDN-SC), as an SDN-based mobility management mechanism that retains session for hosts roaming across subnets in an SDN network. Particularly, SDN-SC suppresses possible address re-configurations with techniques such as gateway spoofing and DHCP lease renewal for mobile hosts away from home. We studied the performance of SDN-SC and compared it with that of MIPv4 and PMIPv6. The results show that SDN-SC outperforms both MIPv4 and PMIPv6 in terms of handover latency.