Abstract: The objective of this paper is to investigate the periodic dynamical behaviors for a class of Memristive Cohen-Grossberg neural networks with time-varying delays. By employing M-matrix theory, differential inclusions theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system was proved.Finally, an illustrative example was given to demonstrate the validity of the theoretical results and the existence of periodic solution and equilibrium point was described visually by graphical simulation.