The engineering components of steel alloys in energy sectors are mostly operated at high-temperature and low-to-moderate stresses. Introducing precipitates by prior aging process is one of the strategies to improve the creep resistance, mainly in the dislocation glide-dominated operating condition. However, the available limited experimental observations show that the precipitates can also degrade the creep performances. Thus, understanding and quantifying the role of precipitates on the high-temperature creep behavior is critical. In this work, an advanced constitutive model within the full-field elasto-visco-plastic fast Fourier transform (EVPFFT) framework is developed to capture the effect of precipitate size and density on the creep responses of grade-91 and 347H alloys. The model calculation finds that the annihilation/depletion of dislocations, which is governed by the precipitates, during the primary-to-secondary transition modulates the creep rates. In turn, based on the rate of dislocation annihilation, increasing precipitate content can either increase or decrease the creep responses.