Automatic target recognition (ATR) in synthetic aperture radar (SAR) images has been widely used in civilian and military fields. Traditional model-based methods and template matching methods do not work well under extended operating conditions (EOCs), such as depression angle variant, configuration variant, and noise corruption. To improve the recognition performance, methods based on convolutional neural networks (CNN) have been introduced to solve such problems and have shown outstanding performance. However, most of these methods rely on continuously increasing the width and depth of networks. This adds a large number of parameters and computational overhead, which is not conducive to deployment on edge devices. To solve these problems, a novel lightweight fully convolutional neural network based on Channel-Attention mechanism, Channel-Shuffle mechanism, and Inverted-Residual block, namely the ASIR-Net, is proposed in this paper. Specifically, we deploy Inverted-Residual blocks to extract features in high-dimensional space with fewer parameters and design a Channel-Attention mechanism to distribute different weights to different channels. Then, in order to increase the exchange of information between channels, we introduce the Channel-Shuffle mechanism into the Inverted-Residual block. Finally, to alleviate the matter of the scarcity of SAR images and strengthen the generalization performance of the network, four approaches of data augmentation are proposed. The effect and generalization performance of the proposed ASIR-Net have been proved by a lot of experiments under both SOC and EOCs on the MSTAR dataset. The experimental results indicate that ASIR-Net achieves higher recognition accuracy rates under both SOC and EOCs, which is better than the existing excellent ATR methods.