We systematically study the mechanical and electronic properties of a novel superhard sp3 carbon allotrope (Imma-carbon). This polymorph was identified using a developed methodology on the theoretical design of superhard material materials based on the CALYPSO algorithm, and predicted to be more stable than graphite for pressures above 12.9 GPa. The structural, electronic, and mechanical properties of Imma -carbon were investigated by means of density functional theory (DFT). It is dynamically stable and a semiconductor with a direct band gap of ∼2.6 eV. The calculated elastic constants for Imma-carbon satisfy the stability condition. Calculations of bulk modulus and hardness indicate that this Imma-carbon is an ultra-incompressible and superhard material. Meanwhile, we extensively investigated stress–strain relations of Imma-carbon under various tensile and shear loading directions. The present results provide insight for understanding its mechanical properties at the atomic level. Our study provides valuable guidance in designing new strong covalent superhard materials.