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Category-level pose estimation is a challenging problem due to intra-class shape variations. Recent methods deform pre-computed shape priors to map the observed point cloud into the normalized object coordinate space and then retrieve the pose via post-processing, i.e., Umeyama's Algorithm. The shortcomings of this two-stage strategy lie in two aspects: 1) The surrogate supervision on the intermediate results can not directly guide the learning of pose, resulting in large pose error after post-processing. 2) The inference speed is limited by the post-processing step. In this paper, to handle these shortcomings, we propose an end-to-end trainable network SSP-Pose for category-level pose estimation, which integrates shape priors into a direct pose regression network. SSP-Pose stacks four individual branches on a shared feature extractor, where two branches are designed to deform and match the prior model with the observed instance, and the other two branches are applied for directly regressing the totally 9 degrees-of-freedom pose and performing symmetry reconstruction and point-wise inlier mask prediction respectively. Consistency loss terms are then naturally exploited to align the outputs of different branches and promote the performance. During inference, only the direct pose regression branch is needed. In this manner, SSP-Pose not only learns category-level pose-sensitive characteristics to boost performance but also keeps a real-time inference speed. Moreover, we utilize the symmetry information of each category to guide the shape prior deformation, and propose a novel symmetry-aware loss to mitigate the matching ambiguity. Extensive experiments on public datasets demonstrate that SSP-Pose produces superior performance compared with competitors with a real-time inference speed at about 25Hz.