Albeit Deep neural networks (DNNs) are widely used in computer vision, natural language processing and speech recognition, they have been discovered to be fragile to adversarial attacks. Specifically, in computer vision, an attacker can easily deceive DNNs by contaminating an input image with perturbations imperceptible to humans. As one of the important vision tasks, face verification is also subject to adversarial attack. Thus, in this paper, we focus on defending against the adversarial attack for face verification to mitigate the potential risk. We learn a network via an implementation of stacked residual blocks, namely adversarial perturbations alleviation network (ApaNet), to alleviate latent adversarial perturbations hidden in the input facial image. During the supervised learning of ApaNet, only the Labeled Faces in the Wild (LFW) is used as the training set, and the legitimate examples and corresponding adversarial examples produced by projected gradient descent algorithm compose supervision and inputs respectively. By leveraging the middle and high layer’s activation of FaceNet, the discrepancy between an image output by ApaNet and the supervision is calculated as the loss function to optimize ApaNet. Empirical experiment results on the LFW, YouTube Faces DB and CASIA-FaceV5 confirm the effectiveness of the proposed defender against some representative white-box and black-box adversarial attacks. Also, experimental results show the superiority performance of the ApaNet as comparing with several currently available techniques.