We propose a long distance measurement-device-independent (MDI) quantum-key-distribution (QKD) with quantum memory, and analyze the relationship between the key generation rate and the storage efficiency of quantum memory. Our protocol is considered and compared with MDI-QKD without quantum memory. We present general formulas for our protocol with three-intensity decoy states. The simulation results show that the maximum secure distance supported by MDI-QKD with quantum memory is about 500 km, while the maximum secure distance of MDI-QKD without quantum memory is only 216 km. With certain limits, prolonging the time of maintaining the necessary quantum fidelity can increase security key transmission distance. Furthermore, the protocol is robust against device imperfection such as quantum memory decoherence effects, which can be easily applied to practical QKD system.