In recent studies, synthetic aperture radar (SAR) automatic target recognition (ATR) algorithms that are based on the convolutional neural network (CNN) have achieved high recognition rates in the moving and stationary target acquisition and recognition (MSTAR) dataset. However, in a SAR ATR task, the feature maps with little information automatically learned by CNN will disturb the classifier. We design a new enhanced squeeze and excitation (enhanced-SE) module to solve this problem, and then propose a new SAR ATR network, i.e., the enhanced squeeze and excitation network (ESENet). When compared to the available CNN structures that are designed for SAR ATR, the ESENet can extract more effective features from SAR images and obtain better generalization performance. In the MSTAR dataset containing pure targets, the proposed method achieves a recognition rate of 97.32% and it exceeds the available CNN-based SAR ATR algorithms. Additionally, it has shown robustness to large depression angle variation, configuration variants, and version variants.