This paper considers the problem of robust stability for uncertain neural networks with time varying delays.The uncertainties considered are norm-bounded uncertainties. These unceitainties of system parameters are associated with time, but the norm is restricted in a certain scope, the time delay function is improved with time, and its derivative is less than one. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a equilibrium point, which is robustly stable. The proposed LMI conditions can be checked easily by recently developed algorithms. A numerical example is given to illustrate the effectiveness of the developed techniques.