The equation of state and vibration properties of TATB crystal were investigated by using the density functional theory (DFT) and combining with van der Walls force correction(vdW-DF2). The partial vibration modes of TATB crystal were reassigned. Vibration mode coupling and the intermolecular interaction process were studied under pressure process up 8.5 GPa. Results show that the NO₂ and NH₂ vibrations were strongly coupled in TATB crystal. The vibration in the wave number range of 1100 cm^-1 to 1500 cm^-1 is particularly complex because of the coupling of NH₂ with NO₂ and benzene ring vibrations. With increasing pressure, TATB molecules from neighboring layers bend and close to each other, causing a coupling of NH₂ plane twist vibration or wag with NO₂ shear vibration, indicating a strengthening of intermolecular hydrogen bonding.