[en] The density and acoustic velocities of a Ce₇₀Al₁₀Ni₁₀Cu₁₀ bulk metallic glass (BMG) under hydrostatic-pressure (up to 0.5 GPa) and in crystallized state in ambient conditions were measured in situ by a pulse echo overlap method. The pressure derivatives of velocities and Grueneisen parameters as well as the equation of state (EOS) of the BMG were determined and compared to those of various other BMGs and nonmetallic glasses. Surprisingly, the BMG, unlike other BMGs with normal mode stiffness, exhibits an anomalous soft longitudinal acoustic mode under pressure similar to that of typical oxide glasses. An unusually large softening of longitudinal acoustic phonons in the BMG, relative to its crystalline state, is also observed, analogous with that in oxide glasses. The possible origin for the anomaly is the intrinsic glassy structure containing short-range covalent bonds