The electronic structures, potential energy surfaces for the displacement of ions along the tetragonal [001] and Γ phonon properties of Na1/2Bi1/2TiO3 and K1/2Bi1/2TiO3 are investigated by employing the first-principles method based on density functional theory. The results indicate that the electronic structures of Na1/2Bi1/2TiO3 and K1/2Bi1/2TiO3 are very similar. The valence band is dominated by O 2p states with an admixture of Ti 3d and Bi 6p states. The lower energy region of the conduction band is mainly composed of Ti 3d orbitals. The bond strengths of Ti–O and Bi–O increase when Na is substituted by K. Moreover, minor differences are observed from the potential energy surface for the displacement of ions along the tetragonal [001], which indicates that the phase instabilities of the two compounds mainly come from the displacement of O ions, which plays a more important role when Na is substituted by K. There are three soft modes for Na1/2Bi1/2TiO3 and K1/2Bi1/2TiO3, which mainly originate from the vibration of O6 group. The A2u soft mode becomes harder when Na is substituted by K.