Abstract: To develop lightweight and high-performance silicon carbide (SiC) primary mirrors， the integration of topology optimization methods with ceramic additive manufacturing techniques provides an effective strategy. The lightweight and thin design method was designed with the back support structure of the primary mirror, with maximum stiffness as the design objective and mass as the constraint. Based on the Heaviside-function based directional growth topology parameterization (H-DGTP) method, a novel method was design while considering the ceramic manufacturability constraints. For typical SiC primary mirror specifications, a lightweight and thin configuration of the primary mirror was obtained that satisfies additive manufacturing requirements. The size optimization method is further adopted to reconstruct and fine-design the topologically optimized mirror structure. Furthermore, a sample primary mirror was fabricated using digital light processing (DLP) additive manufacturing technology, and its manufacturability of additive manufacturing was validated. Numerical simulations of the design scheme showed that the root mean square (RMS) values of the self-weight loads along the x, y and z directions normal to the mirrors were 3.27 nm, 3.27 nm, and 7.55 nm, respectively, with a surface density of 13.21 kg/m2. The analysis results demonstrate that the optimized silicon carbide primary mirror design achieves the target surface accuracy while significantly reducing weight. This study confirms the effectiveness of the proposed method for the lightweight and thin design of additively manufactured SiC space primary mirrors.