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This paper focuses on the hybrid effects of memristor characteristics, coupling coefficient and time-delay on the recurrent neural network. We construct a novel time-delay recurrent neural network based on a passive hyperbolic tangent memristor, whose instability condition at equilibrium points is judged according to the Routh criterion. Under the changes of the memristor internal parameter, coupling coefficient and time-delay, some complex dynamic behaviors, including chaos and various coexisting attractors, of the time-delay memristive recurrent neural network are observed in detail through the bifurcation diagram, the largest Lyapunov exponent, and the basin of attraction. Finally, the theoretical results are verified by the circuit simulation through MULTISIM.