Object detection has been applied in a wide variety of real world scenarios, so detection algorithms must provide confidence in the results to ensure that appropriate decisions can be made based on their results. Accordingly, several studies have investigated the probabilistic confidence of bounding box regression. However, such approaches have been restricted to anchor-based detectors, which use box confidence values as additional screening scores during non-maximum suppression (NMS) procedures. In this paper, we propose a more efficient uncertainty-aware dense detector (UADET) that predicts four-directional localization uncertainties via Gaussian modeling. Furthermore, a simple uncertainty attention module (UAM) that exploits box confidence maps is proposed to improve performance through feature refinement. Experiments using the MS COCO benchmark show that our UADET consistently surpasses baseline FCOS, and that our best model, ResNext-64x4d-101-DCN, obtains a single model, single-scale AP of 48.3% on COCO test-dev, thus achieving the state-of-the-art among various object detectors.