The geometrical and electronic structures, and also the dopant formation energies, lattice constants, band structure and density of states （DOS） of Sr1-xYxTiO3 with x=00, 0125, 025 and 033 are calculated from the first principles of plane wave ultra-soft pseudo-potential method based on density functional theory. The results of dopant formation energy show that Y preferentially enters the Sr site in SrTiO3 Electronic structure results show that pure SrTiO3 is an insulator and the Fermi energy is at the top of valence band. When doped with Y, the Fermi energy of the system goes into the conduction band and the system undergoes an insulator-to-metal transition. Due to the appearance of the carrier impurity from Y doping, there is a significant distortion near the bottommost conduction bands.