A systematic investigation of structural, mechanical, elastic anisotropy and electronic properties of a recently reported novel superhard material orthorhombic C20 (o-C20) under pressure is performed utilizing the density functional theory in this work. The crystal structure parameters are obtained at zero as well as at high pressure. Pressure induced elastic constants Cij, polycrystalline aggregate elastic modulus (B,G,E), B/G ratio, and Debye temperature changes for o-C20 have been determined. The crystal elastic anisotropies of the ultra-incompressible o-C20 are investigated in the pressure range of 0–100 GPa. The Lyakhov–Oganov model is applied to predict the hardness as functions of pressure. The calculated results reveal that o-C20 possesses high elastic anisotropy under zero pressure and high pressure, and the hardness of o-C20 decreases with pressure, while the Debye temperature behaves with the opposite trend. The results of electronic structure indicate that o-C20 exhibits insulator characteristics, and the band gap increases with pressure. This work is expected to provide a useful guide for the future synthesis and application of o-C20.