In this study, Intersecting Tensegrity System that is integrated solid compression members with tension members was presented. This system is set up by connecting upper and lower compression members of pyramid shape with exterior tension members. In this system, the solid compression members are intersected each other and connected by a tension member in the center. This system is a variation of Tensegrity system, has a improved feature that the system is able to induce prestresses in all of tension members easily by adjusting the distance of a tension member in the center. The proposed system was studied by modeling, and the structural behavior of the system was investigated by mechanical analysis of the model. Furthermore, the features of the structural behavior variations was investigated when the composition elements(total height, size of surface, intersection length, etc.) are changed variously. It was also showed that the system is able to be used as a temporary space structure system with a membrane roof of inverse conical shape.