Abstract New structures of body-centered, tetragonal C4 carbon allotropes containing a mixture of sp (triple yne bond) and sp3 (single bond) hybridization were designed using first-principles calculations. These three structures named 1-Yne, 2-Yne and 3-Yne C4 carbon not only maintained the tetragonal space group (SG# 139) of C4 carbon, but also exhibited unique physical and chemical properties due to triple-like bonding. The dynamic stability of these structures was confirmed using phonon calculations, and the entire structure showed a unique phonon spectrum with an Eigen-frequency of ~2250 cm−1, which is a characteristic of a triple bond. Structure prediction by X-ray simulations was performed and the band structure due to triple bond modification was identified. Details of the bulk properties, such as lattice constant, bond length and bulk modulus, could be explained well by a simple physical picture due to the triple bond.