Using first-principles techniques, we investigate the (001) surfaces of cubic PbHfO3 (PHO) and BaHfO3 (BHO) terminated with both AO (A=Pb and Ba) and HfO2- Surface structure, partial density of states, band structure, and surface energy are obtained. The BaO surface is found to be similar to its counterpart in BHO. For the HfO2-terminated surface of cubic PHO, the largest relaxation appears on the second-layer atoms but not on the first-layer ones. The analysis of the structure relaxation parameters reveals that the rumpling of the (001) surface for PHO is stronger than that for BHO. The surface thermodynamic stability is explored, and it is found that both the PbO- and the BaO-terminated surfaces are more stable than the HfO2-terminated surfaces for PHO and BHO, respectively. The surface energy calculations show that the (001) surface of PHO is more easily constructed than that of BHO.