3D face landmarking aims at automatic localization of 3D facial features and has a wide range of applications, including face recognition, face tracking, facial expression analysis. Methods so far developed for pure 2D texture images were shown sensitive to lighting condition changes. In this paper, we present a 3D statistical model-based technique for accurate 3D face landmarking, thus using an "analysis by synthesis" approach. Our 3D statistical model learns from a training set both variations of global 3D face shapes as well as the local ones in terms of scale-free texture and range patches around each landmark. When fitted for a best match to a new 3D face model for analysis, this 3D statistical model delivers the location of the landmarks on the input 3D face model. Experimented on more than 1860 face models from FRGC datasets, our method achieves an average of locating errors less than 7mm for 15 feature points. Compared with a curvature analysis-based method also developed within our team, this learning-based method enables localization of more face landmarks with a general better accuracy at the cost of a learning step.