Abstract In this paper, we investigate a class of impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. By establishing an integro-differential inequality with impulsive initial conditions and applying M -matrix theory, we find some sufficient conditions ensuring the existence, uniqueness, global exponential stability and global robust exponential stability of equilibrium point for impulsive Cohen–Grossberg neural networks with distributed delays and reaction–diffusion terms. An example is given to illustrate the results obtained here.