Category-level object pose estimation requires both global context and local structure to ensure robustness against intra-class variations. However, 3D graph convolution (3D-GC) methods only focus on local geometry and depth information, making them vulnerable to complex objects and visual ambiguities. To address this, we present THE-Pose, a novel category-level 6D pose estimation framework that leverages a topological prior via surface embedding and hybrid graph fusion. Specifically, we extract consistent and invariant topological features from the image domain, effectively overcoming the limitations inherent in existing 3D-GC based methods. Our Hybrid Graph Fusion (HGF) module adaptively integrates the topological features with point-cloud features, seamlessly bridging 2D image context and 3D geometric structure. These fused features ensure stability for unseen or complicated objects, even under significant occlusions. Extensive experiments on the REAL275 dataset show that THE-Pose achieves a 35.8% improvement over the 3D-GC baseline (HS-Pose) and surpasses the previous state-of-the-art by 7.2% across all key metrics. The code is avaialbe on https://github.com/EHxxx/THE-Pose