High-pressure single-crystal / powder synchrotron X-ray diffraction was carried out on a hydrous pure magnesium pyrope (Mg 3 Al 2 Si 3 O 12) containing 900 ppmw H 2 O, synthesized at 4.0 GPa and 1300 K. The pressure-volume (P-V) single-crystal data from room pressure to 9.81 GPa at ambient temperature were fitted by a third-order Birch-Murnaghan equation of state (BM-EoS) yielding a unit-cell volume of V 0 = 1505.14±0.38 Å 3 , an isothermal bulk modulus of K 0 = 160±3GPa and its pressure derivative K′ 0 = 5.2±0.4. When fixing K' 0 =4.0, the data yielded V 0 = 1504.58±0.32 Å 3 and K 0 = 166±2GPa. The pressure-volume-temperature (P-V-T) EoS of the synthetic hydrous pyrope was also measured at temperatures up to 900 K and pressures up to 16.75 GPa, using a diamond anvil cell in conjunction with in situ synchrotron angle-dispersive powder X-ray diffraction. The P-V data at room temperature and in a pressure range of 0.0001-14.81 GPa were then analyzed by a third-order BM-EoS and yielded V 0 = 1505.35±0.25 Å 3 , K 0 = 161±2 GPa, K′ 0 = 5.0±0.3. With K' 0 fixed to 4.0, we also obtained V 0 = 1505.04±0.29 Å 3 and K 0 = 167±1 GPa. Consequently, we fitted the P-V-T data with the high-temperature third-order BM-EoS approach and obtained the thermoelastic parameters of V 0 = 1505.4±0.3 Å 3 , K 0 =162±1 GPa, K′ 0 = 4.9±0.2, the temperature derivative of the bulk modulus (∂K 0 /∂T