Abstract: In this paper, the existence and exponential stability problems of periodic solutions are discussed for a class of Cohen-Grossberg dynamic neural networks with distributed delays and reaction-diffusion terms. Without assuming the boundedness, monotonicity and differentiability of the activation functions, some sufficient conditions are obtained to guarantee the existence and the global exponential stability of periodic solutions for the neural networks with distributed delays and reaction-diffusion terms, based on constructing suitable Lyapunov functional, using M-matrix theory and some inequality techniques. Moreover, several remarks and the comparison with other results in early publication illuminate the advantages of the method. Finally, two numerical examples and the computational simulation are given to validate the theories.