Convolutional neural networks are used to solve problems such as complex data preprocessing, low prediction accuracy, and difficulty in dealing with a large amount of nonlinear data in infrared spectroscopy. Moreover, owing to their strong feature extraction ability and good nonlinear expression ability, the application of convolutional neural networks in the modeling of infrared spectrum analysis has attracted attention. In this study, the advantages of the application of a convolutional neural network for the infrared spectrum are analyzed, and the structure and composition of the convolutional neural network are briefly summarized. Then, the dimension problem of the input data in the spectral analysis modeling of the convolutional neural network is described in detail. This paper reviews the influence of convolution kernel parameters in the model design, multi-task processing model, and optimization methods in the training process. Finally, the advantages and disadvantages of this research are analyzed, and future development trends are discussed.