This paper presents Densely Supervised Grasp Detector (DSGD), a deep learning framework which combines CNN structures with layer-wise feature fusion and produces grasps and their confidence scores at different levels of the image hierarchy (i.e., global-, region-, and pixel-levels). Specifically, at the global-level, DSGD uses the entire image information to predict a grasp. At the region-level, DSGD uses a region proposal network to identify salient regions in the image and uses a grasp prediction network to generate segmentations and their corresponding grasp poses of the salient regions. At the pixel-level, DSGD uses a fully convolutional network and predicts a grasp and its confidence at every pixel. During inference, DSGD selects the most confident grasp as the output. This selection from hierarchically generated grasp candidates overcomes limitations of the individual models. DSGD outperforms state-of-the-art methods on the Cornell grasp dataset in terms of grasp accuracy. Evaluation on a multi-object dataset and real-world robotic grasping experiments show that DSGD produces highly stable grasps on a set of unseen objects in new environments. It achieves 97% grasp detection accuracy and 90% robotic grasping success rate with real-time inference speed.