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The properties of diamond polytypes under high pressure have been investigated by means of the first-principles calculations. They are unveiled to be thermodynamically and kinetically more stable than hexagonal diamond (h-diamond) even under pressure. The electronic and elastic properties of the diamond polytypes are also explored, revealing very close cohesive energy, band gap and equilibrium density to those of cubic diamond (c-diamond). The Vickers hardness is uncovered to be comparable or even larger than those of the c- and h-diamond. Furthermore, they experience lower energy barriers than the h-diamond during the transforming process from graphite under pressure. Especially, we explored the characterized Raman modes under pressure from 0 to 40 GPa for each allotrope, which can be used to identify the diamond polytypes from the c-diamond T 2 g background mode, and the result may serve as a useful guide for future experimental studies. In addition, the simulated X-ray diffraction spectra under pressure is also presented. [ABSTRACT FROM AUTHOR]