Molecular dynamics simulations show that graphite will transform into a superhard phase under cold compression. Recent experiments show that there is a sp 3-rich hexagonal carbon polymorph (a 0=2.496 Å, c 0=4.123Å) with a bulk modulus of 447 GPa and average density about 3.6g/cm 3, restricted to the space group of P-62c (No. 190), but the detailed atomic structure was not obtained [Wang et al., P. Natl. Acad. Sci. 101(38), 13699]. Here we set carbon atoms occupying P-62c 4f Wyckoff positions of P-62c, and calculate the total energy of the different structures changing the internal parameter z by first-principles calculations using geometry optimisation algorithm in CASTEP code, which shows that the stable structures in energy (at local minimum points) are hexagonal carbon (z=1/4) and hexagonal diamond (z=1/16). The calculated mechanical properties and lattice parameters of the structure P-62c 4f (z=1/4) are in good agreement with those of the new hexagonal carbon proposed by Wang et al., which indicates that the atomic structure is a possible candidate.