In recent space missions, high performance antenna such as high surface precision, multi-use frequency and large aperture is required to realize complexed and advanced service mission. Meanwhile, the weight of space structure must be reduced due to limitation of launch vehicle performance. Thus, mesh surface antenna had been developed and employed in a number of missions. In general, the tensile forces of the edge cables become several times greater than those of the center cables. Therefore, the total strain energy of the cables depends on the tensile force distribution including the edge cables. The total strain energy of the cables increases with the number of cables. Consequently, a support structure, e.g., a truss rib structure or a hoop structure, must be sufficiently rigid to prevent deformation of the surface. Thus, reduction of the reflector's weight can be achieved if the tensile force of the cables decreases, while maintaining the required surface accuracy. Therefore, we propose a surface design method in which several compression members are equipped instead of tensile cables. The total strain energy of the cables and the tensile force applied to the support structure can be reduced. However, the actual antenna structure includes cable manufacturing and assembling errors. In this study, we evaluate light weighting effect of the support structure by using an experiment model with adjustment of the surface accuracy. We measure the surface accuracy and cable tension of cable network and axial force and the support structure of a member of bending strain energy. As a result, the total cable strain energy of the cable network with compression members can be decreased and reduce to weight of support structure.