Neural network belongs to complex network, which is studied by many scholars because it can describe all kinds of real systems. Stability is always an important problem of complex network. This paper studies exponential stability of a class of impulsive neural network. In this paper, we establish a generalized Halanay inequality with variable coefficient with distributed delay and impulse. The inequality has three characteristics:it can prove the stability of discontinuous systems with impulse;the coefficient is variable coefficient, and the requirement for the coefficient of inequality is more relaxed, which is more widely used;time delay is distributed time delay. By using the new generalized Halanay inequality and Banach fixed point theory, a simple Lyapunov function is established, and a sufficient condition is obtained for the existence and exponential stability of periodic solutions of impulsive neural networks. It is shown that when the condition is satisfied, the impulsive delay neural networks have unique periodic solutions and the periodic solutions are exponentially stable.