In the field of deep learning, the attention mechanism, as a technology that mimics human perception and attention processes, has made remarkable achievements. The current methods combine a channel attention mechanism and a spatial attention mechanism in a parallel or cascaded manner to enhance the model representational competence, but they do not fully consider the interaction between spatial and channel information. This paper proposes a method in which a space embedded channel module and a channel embedded space module are cascaded to enhance the model’s representational competence. First, in the space embedded channel module, to enhance the representational competence of the region of interest in different spatial dimensions, the input tensor is split into horizontal and vertical branches according to spatial dimensions to alleviate the loss of position information when performing 2D pooling. To smoothly process the features and highlight the local features, four branches are obtained through global maximum and average pooling, and the features are aggregated by different pooling methods to obtain two feature tensors with different pooling methods. To enable the output horizontal and vertical feature tensors to focus on different pooling features simultaneously, the two feature tensors are segmented and dimensionally transposed according to spatial dimensions, and the features are later aggregated along the spatial direction. Then, in the channel embedded space module, for the problem of no cross-channel connection between groups in grouped convolution and for which the parameters are large, this paper uses adaptive grouped banded matrices. Based on the banded matrices utilizing the mapping relationship that exists between the number of channels and the size of the convolution kernels, the convolution kernel size is adaptively computed to achieve adaptive cross-channel interaction, enhancing the correlation between the channel dimensions while ensuring that the spatial dimensions remain unchanged. Finally, the output horizontal and vertical weights are used as attention weights. In the experiment, the attention mechanism module proposed in this paper is embedded into the MobileNetV2 and ResNet networks at different depths, and extensive experiments are conducted on the CIFAR-10, CIFAR-100 and STL-10 datasets. The results show that the method in this paper captures and utilizes the features of the input data more effectively than the other methods, significantly improving the classification accuracy. Despite the introduction of an additional computational burden (0.5 M), however, the overall performance of the model still achieves the best results when the computational overhead is comprehensively considered.