In order to solve the problem that the accuracy of image recognition is not high in the training process of convolutional neural network by using traditional quadratic cost function, a convolutional neural network algorithm based on cross-entropy cost function is proposed. By mathematical derivation, it is proved that the cross-entropy cost function is more accurate than the quadratic cost function in image recognition. Based on MNIST dataset and CIFAR-10 dataset, and using AlexNet convolutional neural network, the quadratic cost function and the cross-entropy cost function are adopted to train the image recognition model respectively. When the recognition accuracy and loss value of the digital image are stable, the cost function is tested several times by using the test data, and comparison is made to the recognition accuracy of the two functions. The simulation results show that the proposed method can not only improve the accuracy of digital image recognition, but also has a faster model training speed than the traditional cost function. The process of training deep neural network model is obviously shortened.