This Letter presents some new sufficient conditions for the uniqueness and global asymptotic stability (GAS) of the equilibrium point for a class of neural networks with multiple constant time delays . It is shown that the use of a more general type of Lyapunov-Krasovskii functional enables us to establish global asymptotic stability of a class of delayed neural networks than those considered in some previous papers. Our results generalize or improve the previous results given in the literature.