In this paper, the problem of vertical handover in software-defined network (SDN) based heterogeneous networks (HetNets) is studied. In the studied model, HetNets are required to offer diverse services for mobile users. Using an SDN controller, HetNets have the capability of managing users access and mobility issues but still have the problems of ping-pong effect and service interruption during vertical handover. To solve these problems, a mobility-aware seamless handover method based on multipath transmission control protocol (MPTCP) is proposed. The proposed handover method is executed in the controller of the software-defined HetNets (SDHetNets) and consists of three steps: location prediction, network selection, and handover execution. In particular, the method first predicts the users location in the next moment with an echo state network (ESN). Given the predicted location, the SDHetNet controller can determine the candidate network set for the handover to pre-allocate network wireless resources. Second, the target network is selected through fuzzy analytic hierarchical process (FAHP) algorithm, jointly considering user preferences, service requirements, network attributes, and user mobility patterns. Then, seamless handover is realized through the proposed MPTCP-based handover mechanism. Simulations using real-world user trajectory data from Korea Advanced Institute of Science & Technology show that the proposed method can reduce the handover times by 10.85% to 29.12% compared with traditional methods. The proposed method also maintains at least one MPTCP subflow connected during the handover process and achieves a seamless handover.