Visual grounding is a task to locate the target indicated by a natural language expression. Existing methods extend the generic object detection framework to this problem. They base the visual grounding on the features from pre-generated proposals or anchors, and fuse these features with the text embeddings to locate the target mentioned by the text. However, modeling the visual features from these predefined locations may fail to fully exploit the visual context and attribute information in the text query, which limits their performance. In this paper, we propose a transformer-based framework for accurate visual grounding by establishing text-conditioned discriminative features and performing multi-stage cross-modal reasoning. Specifically, we develop a visual-linguistic verification module to focus the visual features on regions relevant to the textual descriptions while suppressing the unrelated areas. A language-guided feature encoder is also devised to aggregate the visual contexts of the target object to improve the object's distinctiveness. To retrieve the target from the encoded visual features, we further propose a multi-stage cross-modal decoder to iteratively speculate on the correlations between the image and text for accurate target localization. Extensive experiments on five widely used datasets validate the efficacy of our proposed components and demonstrate state-of-the-art performance.