In recent years, the research of spatial steganalysis based on deep learning has achieved sound results under high embedding rate, but the detection performance under low embedding rate is still not ideal. Therefore, a convolutional neural network structure is proposed, which uses the SRM filter for preprocessing to obtain implicit noise residuals, adopts three convolution layers and designs the size of convolution kernel reasonably, and selects appropriate batch normalization operations and activation functions to improve the network performance. The experimental results show that compared with the existing methods, the proposed network can achieve better detection performance for WOW, S-UNIWARD, and HILL, three common adaptive steganographic algorithms in spatial domain, and significant improvement in detection performance at low embedding rates of 0.2 bpp, 0.1 bpp, and 0.05 bpp. A step-by-step transfer learning method is also designed to further improve the steganalysis effect under low embedding rate conditions.