To achieve strong scalability in global models and accurately simulate atmospheric flows over complex underlying surfaces, unstructured grids have attracted increasing attention due to their flexibility. However, developing high-order numerical models on these complex grids remains a major challenge. In this study, we propose a multi-moment scheme for three-dimensional nonhydrostatic atmospheric dynamics on a hexagonal prism grid. Two kinds of moments, namely the point value and the volume-integrated average, are employed to implement the spatial reconstruction using a single-cell stencil, enabling robust and accurate formulation on unstructured grids. The quadratic reconstruction polynomial is determined by a least-squares approach to minimize asymmetric errors. In the vertical direction, a conservative finite-difference method is employed within a height-based terrain-following coordinate system. Benchmark tests demonstrate that the model achieves third-order accuracy and accurately simulates complex three-dimensional atmospheric flows. The proposed scheme can be readily extended to the icosahedral–hexagonal grid to develop a global atmospheric model. Furthermore, this study establishes a unified multi-moment framework for constructing high-order atmospheric models on fully unstructured meshes.