Category-level object pose estimation, aiming to predict the 6D pose and 3D size of objects from known categories, typically struggles with large intra-class shape variation.Existing works utilizing mean shapes often fall short of capturing this variation.To address this issue, we present SecondPose, a novel approach integrating object-specific geometric features with semantic category priors from DINOv2.Leveraging the advantage of DINOv2 in providing SE(3)-consistent semantic features, we hierarchically extract two types of SE(3)-invariant geometric features to further encapsulate local-to-global object-specific information.These geometric features are then point-aligned with DINOv2 features to establish a consistent object representation under SE(3) transformations, facilitating the mapping from camera space to the pre-defined canonical space, thus further enhancing pose estimation.Extensive experiments on NOCS-REAL275 demonstrate that SecondPose achieves a 12.4\% leap forward over the state-of-the-art.Moreover, on a more complex dataset HouseCat6D which provides photometrically challenging objects, SecondPose still surpasses other competitors by a large margin.The code will be released soon.