In this paper, we consider a class of time-delay artificial neural networks and obtain practical criteria to test asymptotic stability of the equilibrium of the time-delay artificial neural networks, with or without perturbations. These criteria require verification of the definiteness of a certain matrix, or verification of a certain inequality. Furthermore, we discuss the exponential stability and estimate the exponential convergence rate for time-delay artificial neural networks. The applicability of our results is demonstrated by means of two specific examples.