The mechanical properties of carbon fiber composite lattice sandwich structures with tetrahedral truss cores under three-point bending are studied in the present paper. Considering the joint effect of bending of the face sheets and shear of the core, the deflection response of the sandwich structure is derived. The stresses within the face sheets and the truss members are calculated respectively, and the corresponding failure modes are analyzed. Then, collapse mechanism map is conducted to obtain the configuration with the highest mass efficiency. The entire family of optimized designs of composite lattice sandwich structures with tetrahedral truss cores is carried out. It is found that the optimized composite lattice sandwich structures have higher mass efficiency as compared to metallic lattice sandwich structures and composite solid plates. The structural optimized design has a guiding significance for engineering.