This paper investigates the global exponential stability of non-autonomous impulsive and delayed cellular neural networks with periodic coefficients. Particularly, by means of the nonlinear measure method and periodic Halanay differential inequality, we obtain an integral average criterion for global exponential stability of this class of neural networks. Our method does not require assumptions on boundedness and monotonicity of activation functions, which demonstrates that our derived criterion is less restrictive than some existing ones and can be applied to more general practical problems. Moreover, our stability criterion is the generalization and improvement of some existing ones. Finally, an example illustrates the effectiveness of our method and the correctness of our results.