Summary: The general fractional operator shows its great predominance in the construction of constitutive model owing to its agility in choosing the embedded parameters. A generalized fractional viscoelastic-plastic constitutive model with the sense of the \(k\)-Hilfer-Prabhakar \((k-H-P)\) fractional operator, which has the character recovering the known classical models from the proposed model, is established in this article. In order to describe the damage in the creep process, a time-varying elastic element \(E(t)\) is used in the proposed model with better representation of accelerated creep stage. According to the theory of the kinematics of deformation and the Laplace transform, the creep constitutive equation and the strain of the modified model are established and obtained. The validity and rationality of the proposed model are identified by fitting with the experimental data. Finally, the influences of the fractional derivative order \(\mu\) and parameter \(k\) on the creep process are investigated through the sensitivity analyses with two- and three-dimensional plots.