Three new carbon allotropes have been uncovered by compressing hexagonal C20 solid based on density functional tight binding level simulations. They are identified to be energetically more favorable and stable than C20 molecule, with the phase III structure being the energetically most favorable. The volume compression calculations suggest that the phase III has a very high anti-compressibility with a bulk modulus of 427 GPa. All of the predicted structures are semiconductors with varied bandgaps and the phase III has a direct band gap of 5.1 eV. Our results indicate that solid C20 can be converted to a transparent superhard material under cold compression.