We present a deep learning framework, called DuLa-Net, to predict Manhattan-world 3D room layouts from a single RGB panorama. To achieve better prediction accuracy, our method leverages two projections of the panorama at once, namely the equirectangular panorama-view and the perspective ceiling-view, that each contains different clues about the room layouts. Our network architecture consists of two encoder-decoder branches for analyzing each of the two views. In addition, a novel feature fusion structure is proposed to connect the two branches, which are then jointly trained to predict the 2D floor plans and layout heights. To learn more complex room layouts, we introduce the Realtor360 dataset that contains panoramas of Manhattan-world room layouts with different numbers of corners. Experimental results show that our work outperforms recent state-of-the-art in prediction accuracy and performance, especially in the rooms with non-cuboid layouts.