Person search by natural language aims at retrieving a specific person in a large-scale image pool that matches given textual descriptions. While most of the current methods treat the task as a holistic visual and textual feature matching one, we approach it from an attribute-aligning perspective that allows grounding specific attribute phrases to the corresponding visual regions. We achieve success as well as a performance boost by a robust feature learning that the referred identity can be accurately bundled by multiple attribute cues. To be concrete, our Visual-Textual Attribute Alignment model (dubbed as ViTAA) learns to disentangle the feature space of a person into sub-spaces corresponding to attributes using a light auxiliary attribute segmentation layer. It then aligns these visual features with the textual attributes parsed from the sentences via a novel contrastive learning loss. We validate our ViTAA framework through extensive experiments on tasks of person search by natural language and by attribute-phrase queries, on which our system achieves state-of-the-art performances. Codes and models are available at https://github.com/Jarr0d/ViTAA.