As we know, the atmosphere is mainly characterized by its baroclinicity and stratification. The vertical coordinate is crucial for the description of 3D atmospheric motion and thermal-dynamic condition of the static atmosphere. Furthermore, the vertical coordinate is foundation of numerical prediction model construction. Different atmospheric dynamic cores, such as height, pressure and potential temperature-based frames are usually established depending on different vertical coordinate modes. The development of vertical coordinates always contributes to major version update and considerable upgrade of the numerical prediction model. In this paper, we briefly review the history of vertical coordinates for the numerical model. Then, we mainly demonstrate the design art for hybrid vertical coordinates in some operational non-hydrostatic models at home and abroad. Additionally, this paper presents some suggestions on how to select model vertical resolution and prediction variables vertical distribution style. Finally, the progress on arrangement and application of the vertical coordinate for numerical prediction models is summarized and its development tendency is also illustrated.