Experimental and theoretical investigations of quantum tunneling magnetization in the high-spin cluster [Mn12O12(CH3COO)(16)(H2O)(4)].2CH(3)COOH.4H2O under pressure have been performed. The main observation is that the blocking temperature and hysteresis width decrease under the effect of pressure. However, the position of the steps in the magnetization versus field curve does not change noticeably as pressure increases. A theoretical examination of the pressure influence on the relaxation rate and magnetization has been carried out taking into consideration the quantum tunneling effects. The qualitative agreement between theory and experiment has been achieved both at atmospheric and at high pressures. The main conclusion of this analysis is that pressure decreases the blocking temperature, the hysteresis width, and the single ion anisotropy and modifies quantum tunneling magnetization.