Deep learning based face recognition has outperformed traditional methods in many application scenarios. There are two main lines of research to design loss functions for face recognition, i. e., verification and identification. The verification loss functions match the pipeline of open-set face recognition, but it is hard to implement. Therefore, most state-of-the-art deep learning methods for face recognition take the identification loss functions with softmax output units and cross-entropy loss. Nevertheless, identification loss function dose not match the training process with evaluation procedure. A verification loss function is proposed for open-set face recognition to maximize partial area under the Receiver-Operating-Characteristic(ROC) curve, partial Area Under Curve(pAUC). A class-center learning method is also proposed to improve training efficiency, which is critical for the proposed loss function to be comparable to the identification loss in performance. Experimental results on five large scale unconstrained face recognition benchmarks show that the proposed method is highly competitive with state-of-the-art face recognition methods.