Associating image regions with text queries has been recently explored as a new way to bridge visual and linguistic representations. A few pioneering approaches have been proposed based on recurrent neural language models trained generatively (e.g., generating captions), but achieving somewhat limited localization accuracy. To better address natural-language-based visual entity localization, we propose a discriminative approach. We formulate a discriminative bimodal neural network (DBNet), which can be trained by a classifier with extensive use of negative samples. Our training objective encourages better localization on single images, incorporates text phrases in a broad range, and properly pairs image regions with text phrases into positive and negative examples. Experiments on the Visual Genome dataset demonstrate the proposed DBNet significantly outperforms previous state-of-the-art methods both for localization on single images and for detection on multiple images. We we also establish an evaluation protocol for natural-language visual detection.