The passivity, low power consumption, memory characteristics and nanometer size of memristors make them the best choice to simulate synapses in artificial neural networks. In this paper, based on the proposed associative memory rules, we design a memristor neural network with plasticity synapses, which can perform analog operations similar to its biological behavior. For the memristor neural network circuit, we also construct a relatively simple Pavlov’s dog experiment simulation circuit, which can effectively reduce the complexity and power consumption of the network. Some advanced neural activities including learning, associative memory and three kinds of forgetting are realized based on the spiking-rate-dependent plasticity rule. Finally, the Simulation program with integrated circuit emphasis is used to simulate the circuit. The simulation results not only prove the correctness of the design, but also help to realize more efficient, simpler and more complex analog circuit of memristor neural network and then help to realize more intelligent, smaller and low-power brain chips.