Although theoretical works have demonstrated that (0001) polar films of wurtzite (WZ) ZnO automatically transform into graphitic-like (GP) structures, the experimental realization of GP ZnO is limited to a thickness of several atomic layers. Here, using first-principles calculations, we demonstrated that the stability of GP ZnO is closely related to the concentration of near-free carriers. Our results show that the doped carriers, originating from the rich oxygen vacancies, can effectively screen the polar field, and stabilize the WZ structure. Thus, in order to obtain GP ZnO layers with much thicker films, it is necessary to reduce the near-free carrier concentration.