Temperature dependent elastic constants Cij(T) of Cu60Hf30Ti10 bulk metallic glass (BMG) have been investigated in a MHz frequency range using electromagnetic acoustic resonance (EMAR) up to 823 K. At room temperature, the BMG showed high Poisson’s ratio ν arising from low shear modulus G compared with that of constitutive crystalline elements. With increasing temperature, G showed usual linear temperature dependence while it suddenly drops around glass transition temperature, Tg. Within a framework of quasiharmonic approximation, Grüneisen parameter γ around Tg is estimated to be 10. This extremely large γ indicates the high anhramonicity of long wavelength limit acoustic mode phonon in the supercooled liquid state. The unusual elastic behavior can be interpreted on the basis of heterogeneous microstructure.