In order to explore the feasibility of the large lightweight SiC primary mirror, the different lightweight forms were compared and a supporting way for the primary mirror was determined. After theoretically calculating the light weighted structure parameters, a sandwich structure SiC primary mirror with sector holes was designed. With the finite element method, the self-weight deformation for the lightweight mirror upholded by a float support was analyzed. Under the two different conditions, the mirror surface figures were PV=9.43 nm,RMS=2.5 nm and PV=16.7 nm,RMS=3.2 nm, respectively. The results indicated that the influence of the self-weight deformation is smaller while the thermal deformation is larger because of the large coefficient of thermal expansion of SiC. At steady-state temperature field, when temperature changes 1 ℃, the mirror surface figure changes PV=40 nm,RMS=4.8 nm. These results reported here suggest that the thermal control must be applied to the mirror.