Deep Neural Networks (DNNs) have been widely used in Synthetic Aperture Radar Automatic Target Recognition (SAR-ATR) to achieve better performance on SAR image recognition. However, DNNs are known to be vulnerable to adversarial examples, crafted by injecting imperceptible perturbations into clean examples. There is limited research on adversarial attacks for SAR-ATR and most of them focus on white-box attacks, which are impractical in real-world scenarios. Existing works have shown that gradient-based transferable attacks, initially designed for optical images, can effectively enhance the black-box attack performance of adversarial examples. However, we observe that they have rather limited efficacy on SAR images. In this work, we propose a novel gradient-based optimization attack called Sampling-based TEacher Guided (STEG) attack to improve the transferability of SAR adversarial examples. STEG leverages a teacher adversarial example to guide the generation of a student adversarial example by utilizing the ultimate perturbation direction. It stabilizes the update direction by simultaneously incorporating the gradients of both teacher and student adversarial examples during the attack iteration process. Moreover, STEG introduces gradually diminishing random noise to further enhance the attack transferability. Extensive experiments conducted on the MSTAR dataset demonstrate that STEG yields significantly higher performance than other advanced gradient-based transferable attacks in both black-box and white-box settings.