Recent advances in the design of convolutional neural networks have shown that performance can be enhanced by improving the ability to represent multi-scale features. However, most existing methods either focus on designing more sophisticated attention modules, which leads to higher computational costs, or fail to effectively establish long-range channel dependencies, or neglect the extraction and utilization of structural information. This work introduces a novel module, the Multi-Branch Concatenation (MBC), designed to process input tensors and extract multi-scale feature maps. The MBC module introduces new degrees of freedom (DoF) in the design of attention networks by allowing for flexible adjustments to the types of transformation operators and the number of branches. This study considers two key transformation operators: multiplexing and splitting, both of which facilitate a more granular representation of multi-scale features and enhance the receptive field range. By integrating the MBC with an attention module, a Multi-Branch Attention (MBA) module is developed to capture channel-wise interactions within feature maps, thereby establishing long-range channel dependencies. Replacing the 3x3 convolutions in the bottleneck blocks of ResNet with the proposed MBA yields a new block, the Efficient Multi-Branch Attention (EMBA), which can be seamlessly integrated into state-of-the-art backbone CNN models. Furthermore, a new backbone network, named EMBANet, is constructed by stacking EMBA blocks. The proposed EMBANet has been thoroughly evaluated across various computer vision tasks, including classification, detection, and segmentation, consistently demonstrating superior performance compared to popular backbones.