In order to consider quantum transport under the influence of an electron-electron (e-e) interaction in a mesoscopic conductor, the Boltzmann equation and Poisson equation are investigated jointly. The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential conceed with e-e interaction are obtained, and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas-Fermi approximation. Then we apply these results to the tunneling junctions of a metal-insulatorsemiconductor (MIS) in which the electrons are accumulated near the interface of the semiconductor, and we find that the e-e interaction plays an important role in the transport procedure of this system. The electronic density, electric current as well as screening Coulombic potential in this case are studied, and we reveal the time and position dependence of these physical quantities explicitly affected by the e-e interaction.