The superplastic deformation behavior of a fine-grained 7075 Al has been investigated to clarify the issue of threshold stress. A series of mechanical tests has been conducted at various temperatures for the specimens with various grain sizes. The quantitative constitutive parameters have been determined from load relaxation test by applying the internal variable theory of structural superplaticity (SSP) proposed by Chang et al. The GBS flow could be formulated as a viscosity-type equation, characterized by the Newtonian exponent of 1.0. The unresolved issue of threshold stress is clarified and identified as a critical stress required for the GBS. The micro-mechanical roll of grain size refinement has also been manifested in terms of proposed constitutive parameters.