We report on the epitaxial growth and surface structure of infinite-layer cuprate Sr1-xNdxCuO2 films on SrTiO3(001) substrates by combining ozone-assisted molecular beam epitaxy and in situ scanning tunneling microscopy. Careful substrate temperature and flux control has been used to achieve single-phase, stoichiometric, and c-axis oriented films. The surface of the films is usually characterized by a mixed CuO2 surface and gridlike superstructure. The superstructure exhibits a periodicity of 3.47 nm that corresponds to a coincidence lattice between the overlayer peroxide SrO2 and underlying CuO2 plane, and gives rise to a conductance spectrum that is distinct from the Mott-Hubbard band structure of CuO2. At a higher Nd composition x > 0.1, a (2 x 2) surface characteristic of the hole-doped CuO2 emerges, which we ascribe to the intake of apical oxygens in the intervening Sr planes.