We address the problem of weakly-supervised semantic segmentation (WSSS) using bounding box annotations. Although object bounding boxes are good indicators to segment corresponding objects, they do not specify object boundaries, making it hard to train convolutional neural networks (CNNs) for semantic segmentation. We find that background regions are perceptually consistent in part within an image, and this can be leveraged to discriminate foreground and background regions inside object bounding boxes. To implement this idea, we propose a novel pooling method, dubbed background-aware pooling (BAP), that focuses more on aggregating foreground features inside the bounding boxes using attention maps. This allows to extract high-quality pseudo segmentation labels to train CNNs for semantic segmentation, but the labels still contain noise especially at object boundaries. To address this problem, we also introduce a noise-aware loss (NAL) that makes the networks less susceptible to incorrect labels. Experimental results demonstrate that learning with our pseudo labels already outperforms state-of-the-art weakly- and semi-supervised methods on the PASCAL VOC 2012 dataset, and the NAL further boosts the performance.