We describe the target selection and resulting properties of aspectroscopic sample of luminous red galaxies (LRGs) from the imagingdata of the Sloan Digital Sky Survey (SDSS). These galaxies are selectedon the basis of color and magnitude to yield a sample of luminousintrinsically red galaxies that extends fainter and farther than themain flux-limited portion of the SDSS galaxy spectroscopic sample. Thesample is designed to impose a passively evolving luminosity andrest-frame color cut to a redshift of 0.38. Additional, yet moreluminous red galaxies are included to a redshift of ~0.5. Approximately12 of these galaxies per square degree are targeted for spectroscopy, sothe sample will number over 100,000 with the full survey. SDSScommissioning data indicate that the algorithm efficiently selectsluminous (M*g~-21.4) red galaxies, that thespectroscopic success rate is very high, and that the resulting set ofgalaxies is approximately volume limited out to z=0.38. When the SDSS iscomplete, the LRG spectroscopic sample will fill over 1 h-3Gpc3 with an approximately homogeneous population of galaxiesand will therefore be well suited to studies of large-scale structureand clusters out to z=0.5.