Recently, several weakly supervised learning methods have been devoted to utilize bounding box supervision for training deep semantic segmentation models. Most existing methods usually leverage the generic proposal generators (\eg, dense CRF and MCG) to produce enhanced segmentation masks for further training segmentation models. These proposal generators, however, are generic and not specifically designed for box-supervised semantic segmentation, thereby leaving some leeway for improving segmentation performance. In this paper, we aim at seeking for a more accurate learning-based class-agnostic pseudo mask generator tailored to box-supervised semantic segmentation. To this end, we resort to a pixel-level annotated auxiliary dataset where the class labels are non-overlapped with those of the box-annotated dataset. For learning pseudo mask generator from the auxiliary dataset, we present a bi-level optimization formulation. In particular, the lower subproblem is used to learn box-supervised semantic segmentation, while the upper subproblem is used to learn an optimal class-agnostic pseudo mask generator. The learned pseudo segmentation mask generator can then be deployed to the box-annotated dataset for improving weakly supervised semantic segmentation. Experiments on PASCAL VOC 2012 dataset show that the learned pseudo mask generator is effective in boosting segmentation performance, and our method can further close the performance gap between box-supervised and fully-supervised models. Our code will be made publicly available at https://github.com/Vious/LPG_BBox_Segmentation .