We study the surface Andreev bound state (ABS) of superconducting Sr2RuO4, which is a candidate material for the realization of the chiral p-wave superconducting state. In order to clarify the role of chiral edge modes as ABSs, the surface density of states and the tunneling conductance is calculated in the normal metal/Sr2RuO4 junction within the framework of recursive Green’s function method, while taking into account the orbital degrees of freedom (including spin–orbit interactions) with realistic material parameters. In Sr2RuO4, there are two bands α and β originating from quasi-one-dimensional orbitals dyz and dzx and a two-dimensional band γ originating from dxy orbital. We discuss about the contributions of various electronic bands to LDOS and the influence of atomic spin–orbit interaction (SOI). In the light of our calculations, quasi-one-dimensional model with dominant pair potentials in α and β bands is consistent with conductance measurements in Au/Sr2RuO4 junctions.