Abstract: The human brain is a highly complex and large-scale nonlinear dynamic system, and its dynamic behavior is closely related to human intelligent activities. The artificial neural network based on memristors can not only better simulate the working mechanism of human brain, but also its nonlinear characteristics can bring richer dynamic behavior to the neural network. In order to further exploit the advantages of neural networks, a new memristor model with negative resistance is introduced in this paper. This model breaks the restriction of the resistance state polarity of the original memristor, and provides a richer variety of performance for the memristor to act as a neural network synaptic bionic device. A new Hopfield neural network (HNN) based on the memristor model is constructed, which further strengthens the negative feedback function of the Hopfield neural network and makes it exhibit richer and more complex dynamic behaviors. The experimental results show that the new memristive Hopfield neural network has rich dynamic behavior characteristics and some chaotic phenomena. Under the conditions of different values of memristor’s parameters and weight matrix, the changes of phase trajectory and Lyapunov exponent of the system are observed, and comparison with the same type of networks are done, which further proves the effectiveness of the proposed neural network. At the same time, the complex dynamic characteristics also provide research support for applications in data processing and image encryption.