The anatomical landmarking on statistical shape models is widely used in structural and morphometric analyses. The current study focuses on leveraging geometric features to realize an automatic and reliable landmarking. The existing implementations usually rely on classical geometric features and data-driven learning methods. However, such designs often have limitations to specific shape types. Additionally, calculating the features as a standalone step increases the computational cost. In this paper, we propose a convolutional Bayesian model for anatomical landmarking on multi-dimensional shapes. The main idea is to embed the convolutional filtering in a stationary kernel so that the geometric features are efficiently captured and implicitly encoded into the prior knowledge of a Gaussian process. In this way, the posterior inference is geometrically meaningful without entangling with extra features. By using a Gaussian process regression framework and the active learning strategy, our method is flexible and efficient in extracting arbitrary numbers of landmarks. We demonstrate extensive applications on various publicly available datasets, including one brain imaging cohort and three skeletal anatomy datasets. Both the visual and numerical evaluations verify the effectiveness of our method in extracting significant landmarks.