Abstract: In the process of design and implementation of Cohen-Grossberg neural networks, the nonnegative amplification function condition is very practicable. The robust asymptotic stability of a class of Cohen-Grossberg neural networks with nonnegative amplification function and multiple time delays is investigated in case of parameter perturbation. With a useful lemma proved, the relation between global asymptotic stability and robust stability is established. Then with no strictly monotonic increasing quantity and boundedness required for the activation function, a suitable Lyapunov functional is framed properly to give a sufficient and robustly stable criterion in form of linear matrix inequality (LMI) for the equilibrium point of the concerned Cohen-Grossberg neural networks. Simulation result verify the effectiveness of the conclusion.