The convolutional neural network (CNN) has been widely used in image recognition field due to its good performance. This paper proposes a facial expression recognition method based on the CNN model. Regarding the complexity of the hierarchic structure of the CNN model, the activation function is its core, because the nonlinear ability of the activation function really makes the deep neural network have authentic artificial intelligence. Among common activation functions, the ReLu function is one of the best of them, but it also has some shortcomings. Since the derivative of the ReLu function is always zero when the input value is negative, it is likely to appear as the phenomenon of neuronal necrosis. In order to solve the above problem, the influence of the activation function in the CNN model is studied in this paper. According to the design principle of the activation function in CNN model, a new piecewise activation function is proposed. Five common activation functions (i.e., sigmoid, tanh, ReLu, leaky ReLus and softplus–ReLu, plus the new activation function) have been analysed and compared in facial expression recognition tasks based on the Keras framework. The Experimental results on two public facial expression databases (i.e., JAFFE and FER2013) show that the convolutional neural network based on the improved activation function has a better performance than most-of-the-art activation functions.