We have systematically studied the structural, electronic and mechanical properties of a novel superhard sp 3 carbon allotrope ( Amm 2-carbon) based on the density functional theory (DFT). This carbon allotrope was identified using a developed methodology in the theoretical design of superhard materials based on the CALYPSO algorithm, and predicted to be more stable than graphite for pressures above 16.6 GPa. It is found to be dynamically stable and a semiconductor with an insulator with a direct band gap of approximately 4.18 eV. Moreover, the calculated elastic constants for Amm 2-carbon satisfy the stability condition. Calculations of bulk modulus and hardness indicate that this Amm 2-carbon is an ultra-incompressible and superhard material. Furthermore, we extensively investigated the stress-strain relations of Amm 2-carbon under various tensile and shear loading directions. The present results indicate Amm 2-carbon is a superhard material.