Recent advances in computer and information technology have increased the use of 3D models in many fields including medicine, the media, art and entertainment. The great challenge in image processing and computer graphics is to devise computationally efficient and optimal algorithms for recovering images and 3D models contaminated by noise and preserving their geometrical structure. In this paper, the authors propose a regularized kernel diffusion filter for 3D mesh denoising in the weighted graph framework. The proposed approach is able to reduce the over-smoothing effect and effectively remove undesirable noise while preserving prominent geometric features of a 3D mesh such as curved surface regions, sharp edges and fine details. Illustrating experimental results are presented to show the effectiveness of the proposed approach.