The longitudinal velocity V1 and shear velocity Vs of an ultrasonic wave propagated along three arbitrary perpendicular directions of the Zr41.2 Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glass (Zr/Ti BMG) have been measured at ambient pressure, under hydrostatic pressure (up to 0.5 GPa) and uniaxial compression (up to 70 MPa) using the pulse echo overlap method. The third-order elastic constants and the Gruneisen parameter related to the anharmonic properties were derived and discussed. It was found that the BMG with marked different microstructural characteristics, compared with the amorphous carbon, exhibited different behaviours related to shear vibratory under high pressure.