Convolution neural network (CNN) has significantly pushed forward the development of face recognition techniques. To achieve ultimate accuracy, CNN models tend to be deeper or multiple local facial patch ensemble, which result in a waste of time and space. To alleviate this issue, this paper studies a lightened CNN framework to learn a compact embedding for face representation. First, we introduce the concept of maxout in the fully connected layer to the convolution layer, which leads to a new activation function, named Max-Feature-Map (MFM). Compared with widely used ReLU, MFM can simultaneously capture compact representation and competitive information. Then, one shallow CNN model is constructed by 4 convolution layers and totally contains about 4M parameters; and the other is constructed by reducing the kernel size of convolution layers and adding Network in Network (NIN) layers between convolution layers based on the previous one. These models are trained on the CASIA-WebFace dataset and evaluated on the LFW and YTF datasets. Experimental results show that the proposed models achieve state-of-the-art results. At the same time, a reduction of computational cost is reached by over 9 times in comparison with the released VGG model.