The nucleation and growth of dust grains in the stellar envelope are investigated for the case of oxygen-rich stars, where the mass loss occurs as a result of the radiation pressure on the dust grains. The number density of grains, the final grain sizes, and the final amount of metals remaining in gaseous states are calculated based on the grain-nucleation theory proposed by Yamamoto and Hasegawa and Draine and Salpeter. It is shown that, even if we base our calculations on the Lothe-Pound nucleation rate equation instead of the classical, homogeneous nucleation rate equation, the proposed theory gives a number density of grains quite similar to that based on the classical rate equation. The approximate solution of the flow, in this paper, brings physical insight to the problem of how the formation of grains couples the flow passing the sonic point. The metals in the outer envelope remain in gaseous state by the amount of 1--10% of the initial content for the mass-loss rate of 10/sup -5/ M/sub sun/ yr/sup -1/ and by less than 1% for the massloss are less than 3 x 10/sup -6/ M/sub sun/ yr/sup -1/. Species of metals condensed onto the grains are also discussed.