3D telepresence is a next-generation multimedia application, offering remote users an immersive and natural video-conferencing environment with real-time 3D graphics. Kinect sensor, a consumer-grade range camera, facilitates the implementation of some recent 3D telepresence systems. However, conventional data filtering methods are insufficient to handle Kinect depth error because such error is quantized rather than just randomly-distributed. Hence, one could often observe large irregularly-shaped patches of pixels that receive the same depth values from Kinect. To enhance visual quality in 3D telepresence, we propose a novel depth data filtering method for Kinect by means of multi-scale and direction-aware support windows. In addition, we develop a GPU-based CUDA implementation that can perform real-time depth filtering. Results from the experiments show that our method can reconstruct hole-free surfaces that are smoother and less bumpy compared to existing methods like bilateral filtering.