By means of the time-smoothing method developed in the previous papers of this series, the quantum kinetic equation is derived from the principles of statistical mechanics. In this paper, we avoid the BBGKY hierarchy; instead we use the Liouville-von Neumann equation for the time-smoothed density matrix. The Boltzmann distribution function is defined in terms of this time-smoothed density matrix. The present scheme may be applied to strong-coupling systems even if they are not in near equilibrium.