By using low energy electron diffraction (LEED), the atomic structures on Si (113) surfaces were studied. These surfaces were prepared by both ion bombardment followed by annealing (IBA) and epitaxial growth. When tbeannealing temperature was higher than 750℃, a 1 × 1 unreconstructed structure was observed above 600℃ for both kinds of surfaces. Cooling the specimen from the annealing temperature at a rate of 5℃/min, we found that the surface structure converted from the 1×1 through 3×1 (beteen 600℃ and 400℃) to the final 3×2 superstructure. A lower annealing temperature (～600℃) results in a 3×1 superstructure only. Both 3×2 and 3×1 structures are very stable at room temperature. The influence of surface impurities on the Si(113) surface structure was discussed. The clear 3×1 superstructure was also appeared on the initial Si(113) surface of about 20 monolayers thick epitaxial film grown by evaporation method.