Constructing adversarial examples in a black-box threat model injures the original images by introducing visual distortion. In this paper, we propose a novel black-box attack approach that can directly minimize the induced distortion by learning the noise distribution of the adversarial example, assuming only loss-oracle access to the black-box network. The quantified visual distortion, which measures the perceptual distance between the adversarial example and the original image, is introduced in our loss whilst the gradient of the corresponding non-differentiable loss function is approximated by sampling noise from the learned noise distribution. We validate the effectiveness of our attack on ImageNet. Our attack results in much lower distortion when compared to the state-of-the-art black-box attacks and achieves $100\%$ success rate on InceptionV3, ResNet50 and VGG16bn. The code is available at https://github.com/Alina-1997/visual-distortion-in-attack.