Carbon clathrate is a kind of typical carbon allotrope that has an open framework composed of various types of cages, displaying intriguing electronic and mechanical properties. This paper proposes a superhard superstrong carbon clathrate via first-principle calculations. This carbon clathrate, called C60 clathrate, contains 60 carbon atoms buckled through sp3-hybridized bonds in a cubic unit cell with symmetry of Im-3m, and possesses the network topology of commonly called binodal net. C60 clathrate is energetically more stable than fullerene C60 at ambient pressure, and it is more favorable than graphite at a pressure above 50.1 GPa C60 clathrate can be constructed by small C24 cage and flat C18 drum. It shows a high density of 3.34 g/cm3, which is the densest carbon clathrate to date. The estimated Vickers hardness, tensile strength, and shear strength of C60 clathrate reach remarkably high values of 82.8, 90.7, and 76.4 GPa, respectively, indicating its superhard and superstrong characteristic. Band structure calculations indicate that C60 clathrate is semiconductive with a direct band gap of 2.26 eV. C60 clathrate can be potentially used in photovoltaic devices.