We investigated the compressional behavior of i-AlCuFe quasicrystal using diamond anvil cell under quasi-hydrostatic conditions by in situ angle-dispersive X-ray powder diffraction measurements (in both compression and decompression) up to 76 GPa at ambient temperature using neon as pressure medium. These data were compared with those collected up to 104 GPa using KCl as pressure medium available in literature. In general, both sets of data indicate that individual d-spacing shows a continuous decrease with pressure with no drastic changes associated to structural phase transformations or amorphization. The d/d0, where d0 is the d-spacing at ambient pressure, showed a general isotropic compression behavior. The zero-pressure bulk modulus and its pressure derivative were calculated fitting the volume data to both the Murnaghan- and Birch-Murnaghan equation of state models. Results from this study extend our knowledge on the stability of icosahedrite at very high pressure and reinforce the evidence that natural quasicrystals formed during a shock event in asteroidal collisions and survived for eons in the history of the Solar System.