Refraction and specular reflection from transparent objects severely interfere with depth-camera-based 3D measurement, resulting in holes, artifacts and noise in depth maps, which further leads to incomplete object point clouds and biased 6D grasp pose estimation. Existing depth completion methods often struggle to achieve a good trade-off between accuracy and efficiency. To address these issues, this paper proposes spectral and edge-aware depth completion network （SEDNet）, a lightweight depth completion network for robotic grasping. SEDNet first encodes robust joint representations via an RGB-D adaptive gated fusion module. It then employs an edge-aware confidence module to predict a depth confidence map, which suppresses noise in low-confidence regions during multi-scale feature fusion. A shifted-window mechanism is introduced in the downsampling stages to enhance cross-window interaction and preserve structural continuity. On the decoder side, SEDNet combines skip connections with a multi-scale spectral attention module, where differentiable wavelet transforms and dynamic spatial attention enable enhanced reconstruction of fine details and object boundaries. Experiments on the public TransCG dataset demonstrate that, compared with the mainstream baseline depth filler net （DFNet）, our method reduces root-mean-square error (RMSE）, relative error (REL） and mean absolute error (MAE） by 50.00%, 25.93% and 50.00%, respectively, while achieving an inference time of only 0.020 s per frame. These results indicate that SEDNet significantly improves depth completion accuracy while meeting the real-time requirements of robotic grasping, validating the effectiveness and practicality of the proposed method.