The long-distance quantum key distribution network is difficult, since the secure transmission distance of traditional quantum key distribution (QKD) is not long enough. To overcome this problem, A measurement device independent (MDI) QKD protocol based on quantum memories(QM) and entangled photon sources(EPS) is proposed, as well as its network model. And indirectly heralding QM scheme and directly heralding QM with QM scheme based on EPS are compared. The relationships of the key generation rate, secure transmission distance, and hold time of quantum state about MDI-QKD protocol based on QM and EPS are also analyzed. The simulation results show that MDI-QKD based on QM and EPS compensate for the lack of MDI-QKD based on directly heralding QM, which is necessary for heralding QM, and the secure transmission distance is far higher than traditional MDIQKD and general MDI-QKD based on indirectly heralding QM. Furthermore, once the hold time of quantum state is greater than 1 ms, the key generation rate will be almost invariable. The double-channel and two-user network model are employed. The single-channel and multi-user QKD network can be implemented with time division multiplexer and fast optical switch.