Benefited from the proposals of function losses margin-based, face recognition has achieved significant improvements in recent years. Those losses aim to increase the margin between the different identities to enhance the discriminability. Ideally, the class center of different identities is far from each other, and face samples are compact around the corresponding class center. Hence, it's very vital to produce a high-quality class center. However, the distribution of training sets determines the class center. With low-quality samples being in the majority, the class center would be close to the samples with little identity information. As a result, it would impair the discriminability of the learned model for those unseen samples. In this work, we propose a High-Quality Class Center Learning system (HQ2CL). This is an effective system and guides the class center to approach the high-quality samples to keep the discriminability. Specifically, HQ2CL introduces a quality-aware scale and margin layer for the identification loss and constructs a new high-quality center loss. We implement the proposed system without additional burden. And we present the experimental evaluation over different face benchmarks. The experimental results show the superiority of our proposed HQ2CL over the state-of-the-arts.