Continuous dynamic recrystallization (CDRX) forms a new recrystallized microstructure through the progressive increase of low-angle boundary (LAGB) misorientations during plastic deformation of metallic materials (such as aluminum alloys) with high stacking fault energy (SFE), also resulting in the continuous generation and refinement of newborn sub-grains. The present work investigates the effect of deformation parameters on the evolution of the sub-structure and recrystallized microstructure of an AA1050 aluminum alloy during compression at elevated temperatures. The alloy microstructure is investigated under different temperatures, strain rates, and strain, and the recrystallization mechanism is evaluated by analyzing the characteristics of the flow stress, the variation of misorientation angle, and the distribution of sub-grains/recrystallized grains. Then, a constitutive model with a dislocation density-based description of strain hardening is developed to predict the microstructure evolution and macroscopic mechanical response of the alloy. Two different sub-grain size evolution models (Arrhenius-type model and sub-structure-based model) are used with several internal state variables.