This paper presents a new type of viscoplastic model based on viscoelastic convolution integrals for explaining the behavior of asphalt concrete in compression under repeated loading. Triaxial compression cyclic tests carried out for long rest periods, with different loading times and two different pulse shapes, square and haversine, were used in developing and validating the model. These tests demonstrate that the evolution of permanent deformation depends on load history. This history-dependent behavior is not captured accurately by some of the existing Perzyna-type viscoplastic models in which permanent deformation evolution depends on the current values of stress and viscoplastic strain. Therefore, in this study, viscoelastic-like convolution integrals were used in the model to capture the effect of history. The proposed model is applicable to compressive creep and recovery experiments at 54°C with (1) several hundreds of cycles of loading including the secondary creep region, (2) haversine loading shapes at three different peak deviatoric stress levels, 620kPa, 827kPa, and 1034kPa, and square loading shapes at 827kPa peak deviatoric stress, and (3) long rest periods that allow complete viscoelastic recovery.