Synthetic aperture radar (SAR) images often suffer from inadequate attention to target features, insufficient expression of target feature information, and the neglect of phase information in traditional convolutional neural network (CNN) recognition methods. This leads to low recognition accuracy and slow processing speed, which are critical limitations for SAR automatic target recognition (ATR) systems. To overcome these challenges, this paper proposes the multi-scale complexvalued feature attention CNN (MsCvFA-CNN) for SAR ATR. MsCvFA-CNN is a model specifically designed for amplitude and phase information of SAR images. A novel complex-valued attention module (CAM) is proposed in this work to focus on the amplitude and phase characteristics of the target separately. By decoupling the amplitude and phase features, the CAM reduces the training time of the network, while preserving the relevant information. Furthermore, the MsCvFA-CNN employs multiple branches for feature extraction with different kernel sizes, which are then combined with CAM in the fusion stage to improve the network's representation of target features. The proposed MsCvFA-CNN is evaluated on both the complexvalued moving and stationary target acquisition and recognition (MSTAR) dataset, as well as the more challenging dataset for urban interpretation (OpenSARUrban). The results demonstrate that it outperforms traditional networks in terms of recognition accuracy and computational efficiency. Specifically, the use of complex-valued networks results in a 2.23% improvement in recognition accuracy compared to traditional real-valued networks. When CAM is added, the network's accuracy is further improved by 3.21%, and the number of epochs required to achieve the highest accuracy is reduced by nearly half.