Deep Neural Networks (DNNs) are being developed and applied in various image-related tasks. However, their predictions can be easily manipulated by adding small perturbations to the original images, creating adversarial images that are considered difficult for humans to distinguish. This paper proposes an adversarial attack method for black-box models, implemented in two attack phases. The first phase is a full-image attack (L2-loss adversarial attack) to approximate the gradient, using Principal Component Analysis (PCA) or Truncated SVD (Singular Value Decomposition) to reduce the number of queries. The attacked images from this phase are then used to identify important image regions that influence the model’s decision. The second phase attacks the already adversarial images from the first phase, but focuses only on the important regions, aiming to reduce L2-loss. The results on the CIFAR-10 dataset with the ResNet model (92.31% accuracy on the test set) show a 99.22% success rate for targeted attacks and 97% for untargeted attacks. For the ImageNet dataset, the success rate reaches 99% for targeted attacks and 100% for untargeted attacks on the ResNet-50 model (67.83% accuracy on the validation set of ImageNet-1000 subset).