This paper is a study on the nonlinear behavior of polyhedron curved space roof as building structures of quasicrystal system. The quasicrystal is made up of two kinds of parallel hexahedrons, and all the line elements of the parallelepiped have the same length. The quasicrystal design grid dome has a pentagonal symmetry and all members have the same length. This paper described form of design gird dome, and showed the analysis conditions. Also, The displacement-load curve is shown through the analysis and we grasped the flow of the load and forces through analysis of design grid dome applied quasicrystal system.