First-principle calculations of the structural, electronic, vibrational and mechanical properties of the primitive-centered tetragonal boron nitride (pct-BN) structure are performed. Results reveal that pct-BN is more energetically favorable than h-BN above the pressure of 8.8 GPa and dynamically stable at up to 120 GPa. Electronic bonding indicates that pct-BN possesses a covalent character with near-tetrahedral sp³-hybridized electronic states. Vibrational property calculations show that its characteristic sp³ Raman peaks are at 738 cm⁻¹, 1032 cm⁻¹ and 1155 cm⁻¹. The mechanical failure mode of pct-BN is dominated by the shear type. The lowest peak stress of 43.1 GPa under (110) [10] shear sets an upper bound for its ideal strength. The calculated minimum hardness of pct-BN is greater than that of w-BN. Its average hardness approached that of c-BN, indicating that this novel BN allotrope is a potential superhard material.