Convolutional neural network-based methods are attracting increasing attention in steganalysis. However, steganalysis for content-adaptive image steganography in the spatial domain is still a difficult problem. In this paper, a new convolutional neural network-based steganalysis approach was proposed with two contributions. 1) By adding more convolutional layers in the lower part of the model, we proposed a new arrangement of convolutional layers and pooling layers, which can process the local information better than the existing CNN models in steganalysis. 2) By adding the global average pooling layer before the softmax layer instead of using global average pooling before the fully connected layer, the global average pooling was placed in a better position for steganalysis. Two state-of-the-art steganographic algorithms in the spatial domain, namely, WOW and S-UNIWARD, were used to evaluate the effectiveness of our model. The experimental results on BOSSbase showed that the proposed CNN could obtain better steganalysis performance than YeNet across all tested algorithms when the payloads were 0.2, 0.3, and 0.4 bpp.