A numerous MNs can attach to an AP which connects with Mobility Anchor and Access Router (MAAR) of the DMM (Distributed mobility management) may cause overloaded. In this paper, A MEC (Mobile Edge Computing)-based method for early handover over the Fully DMM (MF-DMM) architecture is proposed. The proposed MF-DMM can decide the timing for some MNs to do early handover into a better destined network and also make a selection of which MNs to be moved out for the consideration of load balance. The performance analysis presents that the proposed MF-DMM method has better network performance than the traditional fully DMM method in terms of average queuing delay, the packet delivery time.