The high-pressure properties of the supercritical fluid H-2 have been investigated in the Raman scattering and synchrotron radiation x-ray diffraction experiments at room temperature. The pressure dependence of four vibrational modes, i.e., Q(1)(0), Q(1)(1), Q(1)(2), and Q(1)(3), and four rotational modes, i.e., S-0(0), S-0(1), S-0(2), and S-0(3), were precisely obtained, and three rotational constants under pressure, i.e., B-0, D-0, and H-0, were estimated from theoretical formulas. A peculiar change in the pressure dependence of the Raman spectra was observed at 1-2GPa. Through x-ray experiments, halo patterns were collected within a wide pressure range of 0.1-5GPa, and the molar volume at each pressure was estimated from the d-value of the halo peak. The obtained pressure-volume relation suggested that the fluid H-2 showed a change in compressibility at around 1GPa and became incompressible above this pressure because the repulsive term of the intermolecular potential became dominant. The dependence followed the relational expression of P similar to V-m(-3.11) above 1GPa, whereas fluid O-2 and N-2 of the same homonuclear diatomic molecule followed the relational expression of P similar to V-m(-4.32) above 0.2GPa. It was found that the fluid H-2 behaves differently from fluid O-2 and N-2 and is more easily compressed than those. The behavior of V-m was significantly correlated with the pressure dependence of the Raman spectra, and the peculiar change of the Raman spectra has been attributed to the enhancement of the intermolecular interaction due to the transfer to the solid-like pressure-volume relation.