Although existing person re-identification (Re-ID) methods have shown impressive accuracy, most of them usually suffer from poor generalization on unseen target domain. Thus, generalizable person Re-ID has recently drawn increasing attention, which trains a model on source domains that generalizes well on unseen target domain without model updating. In this work, we propose a novel adaptive domain-specific normalization approach (AdsNorm) for generalizable person Re-ID. It describes unseen target domain as a combination of the known source ones, and explicitly learns domain-specific representation with target distribution to improve the model's generalization by a meta-learning pipeline. Specifically, AdsNorm utilizes batch normalization layers to collect individual source domains' characteristics, and maps source domains into a shared latent space by using these characteristics, where the domain relevance is measured by a distance function of different domain-specific normalization statistics and features. At the testing stage, AdsNorm projects images from unseen target domain into the same latent space, and adaptively integrates the domain-specific features carrying the source distributions by domain relevance for learning more generalizable aggregated representation on unseen target domain. Considering that target domain is unavailable during training, a meta-learning algorithm combined with a customized relation loss is proposed to optimize an effective and efficient ensemble model. Extensive experiments demonstrate that AdsNorm outperforms the state-of-the-art methods. The code is available at: https://github.com/hzphzp/AdsNorm.