The deformation and breakup of a polymer solution droplet plays a key role in inkjet printing technology, tablet-coating process, and other spray processes. In this study, the bag breakup behavior of the polymer droplet is investigated numerically. The simple coupled level set and volume of fluid (S-CLSVOF) method and the adaptive mesh refinement (AMR) technique are employed in the droplet breakup cases at different Weber numbers and Ohnesorge numbers. The nature of the polymer solution is handled using Herschel–Bulkley constitutive equations to describe the shear-thinning behavior. Breakup processes, external flow fields, deformation characteristics, energy evolutions, and drag coefficients are analyzed in detail. For the bag breakup of polymer droplets, the liquid bag will form an obvious reticular structure, which is very different from the breakup of a Newtonian fluid. It is found that when the aerodynamic force is dominant, the increase of the droplet viscous force will prolong the breakup time, but has little effect on the final kinetic energy of the droplet. Moreover, considering the large deformation of the droplet in the gas flow, a new formula with the cross-diameter (D_cro) is introduced to modify the droplet drag coefficient.