<p>The accelerated creep behaviour of rock under varying confining pressures is critical to the long-term stability of rock engineering structures, yet its nonlinear evolution remains difficult to characterize. In this study, triaxial creep tests with coupled confining pressure and pore-water pressure are performed, and the evolution of the viscoplastic strain rate is investigated together with published experimental data. A nonlinear increase in the normalized strain rate with viscoplastic deformation is identified, with a pronounced dependence on confining pressure. On the basis of parameter sensitivity analyses, the viscosity coefficient is identified as the primary parameter governing accelerated creep evolution within the framework of overstress theory. Inspired by the reported correspondence between accelerated creep and the post-peak stage, an internal variable <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> <EquationSource Format="TEX">$\kappa $</EquationSource> </InlineEquation> is introduced to characterize the coupled effects of viscoplastic strain accumulation and confining pressure on accelerated creep evolution. On this basis, an exponential evolution law for viscosity is established, laying the foundation for an improved viscosity-evolution-based Nishihara model. The proposed model can accurately reproduce the key characteristics of rock creep processes and effectively capture the influence of confining conditions on accelerated behaviour. Furthermore, applications to several rock types reported in the literature demonstrate the applicability of the proposed constitutive model to different rock materials after parameter calibration.</p>