In recent years, researchers have been making great progress in the steganalysis technology based on convolution neural networks (CNN). However, experts ignore the contribution of nonlinear residual and joint domain detection to steganalysis, and how to detect the adaptive steganographic algorithms with low embedding rates is still challenging. In this paper, we propose a CNN steganalysis model that uses a joint domain detection mechanism and a nonlinear detection mechanism. For the nonlinear detection mechanism, based on the spatial rich model (SRM), we introduce the maximum and minimum nonlinear residual feature acquisition method into the model to adapt to the nonlinear distribution of steganography information. For the joint domain detection mechanism, we not only apply the high-pass filters from the SRM for spatial residuals, but also apply the patterns from the discrete cosine transform residual (DCTR) for transformation steganographic impacts, so as to fully capture the interference trace of spatial steganography to transform domain. We also apply a new transfer learning method to improve the model's performance. That is, we apply the low embedding rate steganography samples to initialize the model, because we think that the method makes the network more sensitive than applying high embedding rate steganography samples to initialize the model. The simulation results also confirm this assumption. Combined with the above improved methods, the detection accuracy of the model for WOW and S-UNIWARD is higher than that of SRM+EC, Ye-Net, Xu-Net, Yedroudj-Net and Zhu-Net, which is about 4∼6% higher than that of the optimal Zhu-Net. The results can provide a certain reference for steganalysis and image forensics tasks.