Lateral inhibition in top-down feedback is widely existing in visual neurobiology, but such an important mechanism has not be well explored yet in computer vision. In our recent research, we find that modeling lateral inhibition in convolutional neural network (LICNN) is very useful for visual attention and saliency detection. In this paper, we propose to formulate lateral inhibition inspired by the related studies from neurobiology, and embed it into the top-down gradient computation of a general CNN for classification, i.e. only category-level information is used. After this operation (only conducted once), the network has the ability to generate accurate category-specific attention maps. Further, we apply LICNN for weakly-supervised salient object detection.Extensive experimental studies on a set of databases, e.g., ECSSD, HKU-IS, PASCAL-S and DUT-OMRON, demonstrate the great advantage of LICNN which achieves the state-of-the-art performance. It is especially impressive that LICNN with only category-level supervised information even outperforms some recent methods with segmentation-level supervised learning.