The eigenmodes of an electron wave propagating through a Si-quantum wire are analyzed self-consistently by a finite-element method. The anisotropic effective mass tensor corresponding to the three inequivalent alignments of conduction band valleys in Si and the continuity of the probability current densities at the Si– SiO2 interface are taken into account. As a result, the eigenenergies of the electron wave and the electron density distribution are found to be greatly affected by the electron-electron interaction. It is also demonstrated that the number of guided modes in the Si-quantum wire is controlled by the gate bias voltage.