As CNNs have a strong capacity to learn discriminative facial features, CNNs have greatly promoted the development of face recognition, where the loss function plays a key role in this process. Nonetheless, most of the existing loss functions do not simultaneously apply weight normalization, apply feature normalization and follow the two goals of enhancing the discriminative capacity (optimizing intra-class/inter-class variance). In addition, they are updated by only considering the feedback information of each mini-batch, but ignore the information from the entire training set. This paper presents a new loss function called Gico loss. The deep model trained with Gico loss in this paper is then called GicoFace. Gico loss satisfies the four aforementioned key points, and is calculated with the global information extracted from the entire training set. The experiments are carried out on five benchmark datasets including LFW, SLLFW, YTF, MegaFace and FaceScrub. Experimental results confirm the efficacy of the proposed method and show the state-of-the-art performance of the method.