Surface structures and electronic states of SrCuO2 were examined under various temperatures and oxidant flux densities by means of reflection high energy electron diffraction and X-ray photoelectron spectroscopy. A reversible structural phase transition between the (1 X 1) phase and an incommensurate phase was observed for Cu-O terminated surfaces. The transition was found to correlate with the amount of oxygen incorporated in the surface layer, which is in equilibrium with that in the bulk. The surface state of the Cu-O layer under the tetragonal SrCuO2 growth condition exhibits incommensurate structure with Cu in divalent (+2) state, which is in thermodynamic equilibrium with the gaseous oxidant and the bulk.