Distinguishing between geometric features and noise is of paramount importance for mesh denoising. In this paper, a graph-based feature-preserving mesh normal filtering scheme is proposed, which includes two stages: graph-based feature detection and feature-aware guided normal filtering. In the first stage, faces in the input noisy mesh are represented by patches, which are then modelled as weighted graphs. In this way, feature detection can be cast as a graph-cut problem. Subsequently, an iterative normalized cut algorithm is applied on each patch to separate the patch into smooth regions according to the detected features. In the second stage, a feature-aware guidance normal is constructed for each face, and guided normal filtering is applied to achieve robust feature-preserving mesh denoising. The results of experiments on synthetic and real scanned models indicate that the proposed scheme outperforms state-of-the-art mesh denoising works in terms of both objective and subjective evaluations.