Object detection, instance segmentation, and pose estimation are popular visual recognition tasks which require localizing the object by internal or boundary landmarks. This paper summarizes these tasks as location-sensitive visual recognition and proposes a unified solution named location-sensitive network (LSNet). Based on a deep neural network as the backbone, LSNet predicts an anchor point and a set of landmarks which together define the shape of the target object. The key to optimizing the LSNet lies in the ability of fitting various scales, for which we design a novel loss function named cross-IOU loss that computes the cross-IOU of each anchor point-landmark pair to approximate the global IOU between the prediction and ground-truth. The flexibly located and accurately predicted landmarks also enable LSNet to incorporate richer contextual information for visual recognition. Evaluated on the MS-COCO dataset, LSNet set the new state-of-the-art accuracy for anchor-free object detection (a 53.5% box AP) and instance segmentation (a 40.2% mask AP), and shows promising performance in detecting multi-scale human poses. Code is available at https://github.com/Duankaiwen/LSNet