We have designed new structures of carbon allotropes combining a mixture of sp (triple bond) and sp3 (single bond) hybridization through first-principle calculation. These two structures named yne-carbon (Y-carbon) and tetrayne-carbon (TY-carbon), respectively, not only maintained the cubic structure and space group (Fd3̄m) of diamond but were also energetically more stable than recently proposed carbon allotrope, T-carbon. A phonon calculation revealed these structures to be stable, and the nature of the triple bond was illustrated by the unique phonon spectrum with an eigen-frequency of 2200 cm -1. The band gap of Y-carbon was found to be larger than that of diamond, whereas the band gap of TY-carbon was smaller than that of T-carbon, which is closely related to the properties of a carbon tetrahedron. The existence of triple bonding of carbon is associated with a dimerization phenomenon due to Peierls instability.