The exponential stability characteristics of the Cohen-Grossberg neural networks with discrete delays are studied in this paper, without assuming the symmetry of connection matrix as well as the monotonicity and differentiability of the activation functions and the self-signal functions. By constructing suitable Lyapunov functionals, the delay-independent sufficient conditions for the networks converge exponentially toward the equilibrium associated with the constant input are obtained. It does not doubt that our results are significant and useful for the design and applications of the Cohen-Grossberg neural networks.