Recently, the unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) has become a highly sought-after topic for its wide applications in target recognition, detection, and tracking. However, SAR automatic target recognition (ATR) models based on deep neural networks (DNN) are suffering from adversarial examples. Generally, non-cooperators rarely disclose any SAR-ATR model information, making adversarial attacks challenging. To tackle this issue, we propose a novel attack method called Transferable Adversarial Network (TAN). It can craft highly transferable adversarial examples in real time and attack SAR-ATR models without any prior knowledge, which is of great significance for real-world black-box attacks. The proposed method improves the transferability via a two-player game, in which we simultaneously train two encoder–decoder models: a generator that crafts malicious samples through a one-step forward mapping from original data, and an attenuator that weakens the effectiveness of malicious samples by capturing the most harmful deformations. Particularly, compared to traditional iterative methods, the encoder–decoder model can one-step map original samples to adversarial examples, thus enabling real-time attacks. Experimental results indicate that our approach achieves state-of-the-art transferability with acceptable adversarial perturbations and minimum time costs compared to existing attack methods, making real-time black-box attacks without any prior knowledge a reality.