Abstract: The memory characteristics of Hopfield neural network are related to the shape of the attractive basin of the stable equilibrium points of the system. This paper studies the memory characteristics of two-neuron Hopfield neural network. Firstly,the distribution and stability of the equilibrium points are obtained with different system parameter values. Then,on the basis of numerical method,the attractive basin of stable equilibrium points is obtained. It is indicated there can be multiple stable equilibrium points,and the shape of the attractive basin of those stable equilibrium points varies with the variation of system parameters.