The lattice structures and the electronic structures of different ordered structures in Ba0.5Sr0.5TiO3 are calculated by the first-principles method. The results of geometry structures and overlap populations reveal that the BST100 ordered structure is tetragonal. The O atoms in Ti-O octahedron parallel to Ba plane and Sr plane are shifted ward Sr plane by 0.065 Å. And the Ti atom in Ti-O octahedron has a off-center displacement of 0.040 Å. The off-center displacements of O atoms and Ti atoms result in the distortion of Ti-O octahedron, and the occurrence of antiparallel spontaneous polarization. Therefore the BST100 ordered structure is in antiferroelectric phase. The O atoms in BST110 ordered structure also have a off-center displacement of 0.029 Å, while the Ti atom in Ti-O octahedron is still in-center. This tetragonal structure is in paraelectric phase. The BST111 ordered structure is in cubic paraelectric phase. The calculated density of states shows that the hybridization between Ti 3d and O 2p plays a primary role in the generation of ferroelectricity. The results of the present work imply that the local order of A site can significantly influences the structural phase transition of disordered BST solid solution.