Tensile and compressive creep behavior of propellants in solid motors due to the influence of the gravity and long-term storage might affect the interior ballistics and structural integrity. In order to investigate the change trends of tensile and compressive creep for HTPB propellant, the 1 000 s tensile, 1 000 s compression and 28 d tensile creep tests were designed and carried out in this work. Meanwhile, the Saint-Venant body and the compressive-tensile asymmetry factor were introduced to establish a propellant viscoelastic plastic constitutive model that takes into account compressive-tensile asymmetry. The range of application of this equation was obtained by fitting and analyzing the parameters in the constitutive equation. The results indicate that the compressive creep process of propellant was mainly dependent on stress level. At the same stress level, viscoelastic deformation of tensile creep is about 1.62 times that of compressive creep, while compressive yield stress is 3.82 times that of tensile yield stress. The tension-compression asymmetric viscoelastic plastic constitutive model can well characterize the tensile-compression creep response of propellants at the lower stress levels. The conclusions and research method in this work can provide reference for structural integrity analysis and storage life evaluation of solid motor.