This paper proposes a four-dimension HNN under time delay via a memristor synapse to imitate the electromagnetic induction current caused by membrane potential difference between two adjacent neurons. Furthermore， we investigate stability of the equilibrium solution the system and the activation condition of Hopf bifurcation if turning instable. Moreover， we analyze the dynamic changes of the system for different time delays and different memristive coupling strengths with fixed time delays. Numerical simulations reveal complex dynamic phenomena， such as limit cycles， chaotic attractors， etc.