Based on first-principles calculations we investigated the structural and electronic properties for a new carbon phase with body-centered tetragonal structure, bct-C-4. The single-elastic constants calculations reveal that bct-C-4 is mechanically stable under ambient conditions, being consistent with a previous theoretical study. The predicted bulk and shear moduli are 396 GPa and 423 GPa, respectively. The calculated ideal tensile strengths are 80.3 GPa and 130.4 GPa along the < 100 > and < 001 > directions, respectively. The theoretical Vickers hardness of bet-C-4 was estimated as 88 GPa, which is comparable to that of diamond.