The pressure cure process of solid propellant grains involves complex thermo-chemo-mechanical coupled effects, leading to empirical design and monotonous pressure control in engineering practice, which restricts technological advancement. To address this issue, a three-dimensional viscoelastic constitutive model and its incremental equations were established considering the coupled effects of curing reaction heat, cure volume shrinkage, and viscoelastic evolution derived from thermo-rheologically complex material behavior. The influences of multi-field coupled effects, thermo-rheologically complex material behavior, cure reaction exothermy, cure volume shrinkage coefficient, and pressure on the pressure cure process were analyzed. Results indicate that multi-field coupled effects significantly impact cure residual stress, and neglecting thermo-rheologically complex material behavior results in underestimation of cure residual stress. Partial pressure unloading during the cure stage effectively reduces cure residual stress. The findings provide theoretical support for optimizing the pressure cure process of solid propellant grains.