Face recognition algorithms based on deep learning methods have become increasingly popular. Most of these are based on highly precise but complex convolutional neural networks (CNNs), which require significant computing resources and storage, and are difficult to deploy on mobile devices or embedded terminals. In this paper, we propose several methods to improve the algorithms for face recognition based on a lightweight CNN, which is further optimized in terms of the network architecture and training pattern on the basis of MobileFaceNet. Regarding the network architecture, we introduce the Squeeze-and-Excitation (SE) block and propose three improved structures via a channel attention mechanism—the depthwise SE module, the depthwise separable SE module, and the linear SE module—which are able to learn the correlation of information between channels and assign them different weights. In addition, a novel training method for the face recognition task combined with an additive angular margin loss function is proposed that performs the compression and knowledge transfer of the deep network for face recognition. Finally, we obtained high-precision and lightweight face recognition models with fewer parameters and calculations that are more suitable for applications. Through extensive experiments and analysis, we demonstrate the effectiveness of the proposed methods.