As the deep learning makes big progresses in still-image face recognition, unconstrained video face recognition is still a challenging task due to low quality face images caused by pose, blur, occlusion, illumination etc. In this paper we propose a network for face recognition which gives an explicit and quantitative quality score at the same time when a feature vector is extracted. To our knowledge this is the first network that implements these two functions in one network online. This network is very simple by adding a quality network branch to the baseline network of face recognition. It does not require training datasets with annotated face quality labels. We evaluate this network on both still-image face datasets and video face datasets and achieve the state-of-the-art performance in many cases. This network enables a lot of applications where an explicit face quality scpre is used. We demonstrate three applications of the explicit face quality, one of which is a progressive feature aggregation scheme in online video face recognition. We design an experiment to prove the benefits of using the face quality in this application. Code will be available at url{https://github.com/deepcam-cn/facequality}.