Solid rocket propellants based on hydroxyl-terminated polybutadiene (HTPB), in which HTPB acts as the polymeric binder and fuel matrix, are widely used in aerospace propulsion. During storage, transport, and service, these composite energetic materials are exposed to sustained mechanical loads as well as environmental variations, which may induce time-dependent inelastic deformation. Such creep deformation can alter the grain geometry, affect combustion stability, and reduce the structural reliability of rocket motors. In this work, room-temperature tensile creep tests were conducted on an HTPB-based solid propellant under different stress levels. Several viscoelastic and power-law constitutive models were compared, and a composite time-hardening creep model was established to describe the experimental strain–time response. The model was further implemented in Abaqus through a Fortran user subroutine for finite element simulation. The results provide a useful basis for creep deformation assessment, formulation optimization, and structural reliability analysis of HTPB-based propellants.