The energetic stability, the structural and the electronic properties of rhombohedral and tetragonal PbZr0.5Ti0.5O3 are systematically investigated by the first-principles plane-wave pseudopotential and the virtual crystal approximation (VCA) based on the density functional theory, within the frameworks of local density approximation (LDA) and generalized gradient approximation (GGA). Our calculation results show that the total energy of the rhombohedral phase is lower than that of the tetragonal phase, which suggests that the rhombohedral structure is more energetically stable than the tetragonal one. Furthermore, the structural parameters calculated in the GGA are well consistent with experimental values. From the analysis of electronic structure, we can find the strong hybridization between Ti/Zr d and O 2p both in two phases. Furthermore the hybridization between Ti-O is stronger than that between Zr-O; there also exists the hybridization between Pb s, d and O 2s, 2p. Moreover, the hybridization between Pb 5d and O 2s in the rhombohedral phase is stronger than that in the tetragonal phase, which indicates that the rhombohedral phase is more stable than the tetragonal phase.