Convolutional neural networks (CNN) have been widely used in the field of synthetic aperture radar (SAR) image classification for their high classification accuracy. However, because CNNs learn a fairly discontinuous input-output mapping, they are vulnerable to adversarial examples. Unlike most existing attack manners that fool CNN models with complex global perturbations, this study provides an idea for generating more dexterous adversarial perturbations. It demonstrates that minor local perturbations are also effective for attacking. We propose a new attack method called local aggregative attack (LAA), which is a black-box method based on probability label information, to reduce the range and amplitude of adversarial perturbations. Our attack introduces the differential evolution (DE) algorithm to search for the optimal perturbations and applies the maximum between-class variance method (OTSU algorithm) to accomplish pixel-level labelling of the target and background areas, enabling attackers to generate adversarial examples of SAR images (AESIs) by adding small-scale perturbations to specific areas. Meanwhile, the structural dissimilarity (DSSIM) metric optimises the cost function to limit image distortion and improve attack stealthiness. Experiments show that our method achieves a high attack success rate against these CNN-based classifiers, and the generated AESIs are equipped with non-negligible transferability between different models.