The correlation between the internal friction behaviour of Zr55Al10Ni5Cu30 BMG samples and their quenching temperatures was investigated. It was found that, below the glass transition temperature, the activation energy decreased with increasing quenching temperature, but in the surpercooled liquid region the activation energy tended to be enhanced with a further increase in the quenching temperature. Besides, there were both anelastic and viscoelastic relaxation for the amorphous alloys. The anelastic behaviour would change into viscoelastic relaxation easily for the samples prepared at higher temperature.