A Minimum Bounding Sector model (MBS) is proposed which represents the direction relationship on hemispherical surface. The model projects the region on the hemispherical surface to the bottom and divides the bottom region into 12 atom areas based on the projection of the region on the hemispherical surface. In this way, the model not only represents the direction relations such as left and right, but also represents the height information qualitatively by means of the distance between the points and the center on the projection plane. And the 1932 cases that exists in the MBS is also represented. As to the further research on reasoning and the composition table, the relational matrix is proposed through which the direction relations between regions on the hemispherical surface are deduced conveniently.