Infrared images have been widely used in many research areas, such as target detection and scene monitoring. Therefore, the copyright protection of infrared images is very important. In order to accomplish the goal of image-copyright protection, a large number of image-steganography algorithms have been studied in the last two decades. Most of the existing image-steganography algorithms hide information based on the prediction error of pixels. Consequently, reducing the prediction error of pixels is very important for steganography algorithms. In this paper, we propose a novel framework SSCNNP: a Convolutional Neural-Network Predictor (CNNP) based on Smooth-Wavelet Transform (SWT) and Squeeze-Excitation (SE) attention for infrared image prediction, which combines Convolutional Neural Network (CNN) with SWT. Firstly, the Super-Resolution Convolutional Neural Network (SRCNN) and SWT are used for preprocessing half of the input infrared image. Then, CNNP is applied to predict the other half of the infrared image. To improve the prediction accuracy of CNNP, an attention mechanism is added to the proposed model. The experimental results demonstrate that the proposed algorithm reduces the prediction error of the pixels due to full utilization of the features around the pixel in both the spatial and the frequency domain. Moreover, the proposed model does not require either expensive equipment or a large amount of storage space during the training process. Experimental results show that the proposed algorithm had good performances in terms of imperceptibility and watermarking capacity compared with advanced steganography algorithms. The proposed algorithm improved the PSNR by 0.17 on average with the same watermark capacity.