Person re-identification (re-ID) is the task of matching the same individuals across multiple cameras, and its performance is greatly influenced by background clutter. Most re-ID methods remove background clutter using hard manners, such as the use of segmentation algorithms. However, the hard manner may damage the structure information and smoothness of original images. In this work, we propose a unidirectional information-interaction network (UI²N) that consists of a global stream (G-Stream) and a background-graying stream (BGg-Stream). The G-Stream and BGg-Stream carry out unidirectional information interaction such that their features are complementary. We further propose a soft manner with the UI²N to weaken background clutter by background-graying. The soft manner can help the UI²N filter out background interference and retain some informative background cues. Extensive evaluations demonstrate that our method significantly outperforms many state-of-the-art approaches in the challenging Market-1501, DukeMTMC-reID, and CUHK03-NP datasets.