Abstract: The global asymptotical robust stability of neural networks with time-varying delays is investigated. Based on nonnegative matrix theory and Lyapunov-Razumikhin technique, a sufficient condition for global asymptotical robust stability is given, which is independent of time delays and can be verified easily. Theoretical analysis and numerical examples show that the obtained condition generalizes two corresponding results derived in the literatures, and complements the results concerning the robust stability research of neural networks effectively. A numerical example and the corresponding computer simulation are presented to verify the effectiveness of the obtained result.