Point-in-spherical-polygon tests are highly required in global data processing. For this reason, this study proposes an adaptive hexagonal hierarchical grid, which overcomes the difficulty of existing hexagonal hierarchical grids in adaptively subdividing grid cells, and applies it to point-in-spherical-polygon tests. First, the initial spherical hexagonal grid is built by uniformly partitioning a sphere using a regular icosahedron. Then, hierarchical grids are constructed by adaptively subdividing hexagonal cells according to whether a grid contains many polygon edges. As a result, the cells not subdivided contain no or only a few edges, called leaf cells. Finally, pre-computing is performed to determine the location attributes (inside/outside the polygon) of such cells or their center points. In the hierarchical structures, the topologies of related points, edges and faces between adjacent hexagonal grid levels are recorded, by which the leaf cells can be quickly located. For a test point, the leaf cell containing it is found quickly, and then whether it is located in the polygon is determined according to the local situation of the cell. Experimental results show that the proposed method has more stable and efficient performance than the existing methods.