By using the first-principles method, we study the relative stabilities and the thermal ionization energies of the doped Li (LiZn) in the different atomic layers for both the non-polar and polar surfaces. Our calculations indicate that the LiZn in the surface region is more stable than in the ZnO bulk, and the thermal ionization energy of the LiZn in the surface region is considerably bigger than in the ZnO bulk. So, the surface of ZnO film degrades the p-type conductivity of the Li-doped film significantly, which is important for the p-type doping in the low-dimensional ZnO system. Furthermore, we find that the observed difference in thermal ionization energy of LiZn between a surface and bulk actually stems from the different distributions of the electrostatic potentials between a surface and bulk.R66