The curing reaction of hydroxyl-terminated polybutadiene (HTPB) solid propellant slurry alters its internal molecular structure, leading to variations in rheological properties. This study investigates the evolution of the rheological behaviour of HTPB propellant slurry during the curing process. Rheological parameters of the slurry at different curing stages were measured using a rotational rheometer, and its time-dependent rheological characteristics were systematically analysed. Building upon the Herschel–Bulkley–Papanastasiou (HBP) viscosity model, a temporal variable was innovatively incorporated to extend the model into the time domain, resulting in the development of the Herschel–Bulkley–Papanastasiou–Wang (HBPW) constitutive viscosity model. Model parameters were determined through experimental data, and the accuracy of the HBPW model was rigorously validated by comparing numerical simulations with experimental results. The findings demonstrate that the HBPW model effectively captures the viscosity variation patterns of HTPB propellant slurry with respect to both shear rate and curing time, exhibiting a minimal discrepancy of 1.7525% between simulations and experimental data. This work establishes a novel theoretical framework for analysing the rheological properties of HTPB propellant slurry, providing a scientific foundation for optimised propellant formulation design and processing techniques.