Point cloud completion aims to recover the completed 3D shape of an object from its partial observation. A common strategy is to encode the observed points to a global feature vector and then predict the complete points through a generative process on this vector. Nevertheless, the results may suffer from the high-quality shape generation problem due to the fact that a global feature vector cannot sufficiently characterize diverse patterns in one object. In this paper, we present a new shape completion architecture, namely AnchorFormer, that innovatively leverages pattern-aware discriminative nodes, i.e., anchors, to dynamically capture regional information of objects. Technically, AnchorFormer models the regional discrimination by learning a set of anchors based on the point features of the input partial observation. Such anchors are scattered to both observed and unobserved locations through estimating particular offsets, and form sparse points together with the down-sampled points of the input observation. To reconstruct the fine-grained object patterns, AnchorFormer further employs a modulation scheme to morph a canonical 2D grid at individual locations of the sparse points into a detailed 3D structure. Extensive experiments on the PCN, ShapeNet-55/34 and KITTI datasets quantitatively and qualitatively demonstrate the efficacy of AnchorFormer over the state-of-the-art point cloud completion approaches. Source code is available at https://github.com/chenzhik/AnchorFormer.