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.