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Category-level object pose estimation aims to predict the 6D pose as well as the 3D metric size of arbitrary objects from a known set of categories. Recent methods harness shape prior adaptation to map the observed point cloud into the canonical space and apply Umeyama algorithm to recover the pose and size. However, their shape prior integration strategy boosts pose estimation indirectly, which leads to insufficient pose-sensitive feature extraction and slow inference speed. To tackle this problem, in this paper, we propose a novel geometry-guided Residual Object Bounding Box Projection network RBP-Pose that jointly predicts object pose and residual vectors describing the displacements from the shape-prior-indicated object surface projections on the bounding box towards the real surface projections. Such definition of residual vectors is inherently zero-mean and relatively small, and explicitly encapsulates spatial cues of the 3D object for robust and accurate pose regression. We enforce geometry-aware consistency terms to align the predicted pose and residual vectors to further boost performance.