Recently, unsupervised adversarial training (AT) has been extensively studied to attain robustness with the models trained upon unlabeled data. To this end, previous studies have applied existing supervised adversarial training techniques to self-supervised learning (SSL) frameworks. However, all have resorted to untargeted adversarial learning as obtaining targeted adversarial examples is unclear in the SSL setting lacking of label information. In this paper, we propose a novel targeted adversarial training method for the SSL frameworks. Specifically, we propose a target selection algorithm for the adversarial SSL frameworks; it is designed to select the most confusing sample for each given instance based on similarity and entropy, and perturb the given instance toward the selected target sample. Our method is readily applicable to general SSL frameworks that only uses positive pairs. We validate our method on benchmark datasets, on which it obtains superior robust accuracies, outperforming existing unsupervised adversarial training methods.