Pretrained models from self-supervision are prevalently used in fine-tuning downstream tasks faster or for better accuracy. However, gaining robustness from pretraining is left unexplored. We introduce adversarial training into self-supervision, to provide general-purpose robust pretrained models for the first time. We find these robust pretrained models can benefit the subsequent fine-tuning in two ways: i) boosting final model robustness; ii) saving the computation cost, if proceeding towards adversarial fine-tuning. We conduct extensive experiments to demonstrate that the proposed framework achieves large performance margins (eg, 3.83% on robust accuracy and 1.3% on standard accuracy, on the CIFAR-10 dataset), compared with the conventional end-to-end adversarial training baseline. Moreover, we find that different self-supervised pretrained models have diverse adversarial vulnerability. It inspires us to ensemble several pretraining tasks, which boosts robustness more. Our ensemble strategy contributes to a further improvement of 3.59% on robust accuracy, while maintaining a slightly higher standard accuracy on CIFAR-10. Our codes are available at https://github.com/TAMU-VITA/Adv-SS-Pretraining.