Adversarial example detection, which can be conveniently applied in many scenarios, is important in the area of adversarial defense. Unfortunately, existing detection methods suffer from poor generalization performance, because their training process usually relies on the examples generated from a single known adversarial attack and there exists a large discrepancy between the training and unseen testing adversarial examples. To address this issue, we propose a novel method, named Adversarial Example Detection via Principal Adversarial Domain Adaptation (AED-PADA). Specifically, our approach identifies the Principal Adversarial Domains (PADs), i.e., a combination of features of the adversarial examples from different attacks, which possesses large coverage of the entire adversarial feature space. Then, we pioneer to exploit multi-source domain adaptation in adversarial example detection with PADs as source domains. Experiments demonstrate the superior generalization ability of our proposed AED-PADA. Note that this superiority is particularly achieved in challenging scenarios characterized by employing the minimal magnitude constraint for the perturbations.