Several novel stability conditions for BAM neural networks with time-varying delays are studied. Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach, the delay-dependent linear matrix inequality (LMI) conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks. These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs. A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.