Abstract In this paper, a periodic Cohen–Grossberg neural networks with varying delay is considered. Under the generalization of dropping the boundedness and differentiability hypotheses for activation functions as well as differentiability of the varying delays with derivative not greater than 1, some novel sufficient conditions are given to guarantee the existence and global exponential stability of periodic solutions. Our results obtained here improve and extend some previously related results. In addition, two examples are also to illustrate the theory.