We discuss the gauge dependence of physical parameter’s definitions under the on-shell and the polemass renormalization prescriptions.By two-loop-level calculations we prove for the first time that the on-shell massrenormalization prescription makes physical result gauge dependent.On the other hand,such the gauge-dependencedoes not appear in the result of the pole mass renormalization prescription.Our calculation also shows the gaugedependence induced by the on-shell mass renormalization prescription cannot be neglected at two-loop level. We discuss the gauge dependence of physical parameter’s definitions under the on-shell and the polemass renormalization prescriptions .By two-loop-level calculations we prove for the first time that the on-shell mass normalization prescription makes physical result gauge dependent. On the other hand , such the gauge-dependencedoes not appear in the result of the pole mass renormalization prescription. Our calculation also shows the gaugedependence induced by the on-shell mass renormalization prescription can not be neglected at two-loop level.