Deep embedding based text-independent speaker verification has demonstrated superior performance to traditional methods in many challenging scenarios. Its loss functions can be generally categorized into two classes, i.e., verification and identification. The verification loss functions match the pipeline of speaker verification, but their implementations are difficult. Thus, most state-of-the-art deep embedding methods use the identification loss functions with softmax output units or their variants. In this paper, we propose a verification loss function, named the maximization of partial area under the Receiver-operating-characteristic (ROC) curve (pAUC), for deep embedding based text-independent speaker verification. We also propose a class-center based training trial construction method to improve the training efficiency, which is critical for the proposed loss function to be comparable to the identification loss in performance. Experiments on the Speaker in the Wild (SITW) and NIST SRE 2016 datasets show that the proposed pAUC loss function is highly competitive with the state-of-the-art identification loss functions.