Estimating the 6 degrees-of-freedom (6DoF) pose of an object from a single image is an important task in computer vision. Many recent works have addressed it by establishing 2D-3D correspondences and then applying a variant of the PnP algorithm. However, it is extraordinarily difficult to establish accurate 2D-3D correspondences for 6D pose estimation. In this work, we consider 6D pose estimation as a follow-up task to normal estimation so that pose estimation can benefit from the advance of normal estimation. We propose a novel 6D object pose estimation method, in which normal maps rather than 2D-3D correspondences are leveraged as alternative intermediate representations. In this paper, we illustrate the advantages of using normal maps for 6D pose estimation and also demonstrate that the estimated normal maps can be easily embedded into common pose recovery methods. On LINEMOD and LINEMOD-O, our method easily surpasses the baseline method and outperforms or rivals the state-of-the-art correspondence-based methods on common metrics. Our code is made publicly available.