Whether the terrestrial planets accreted in the presence of the solar nebula or not has been a major uncertainty in the formation of the solar system. In gaseous accretion, a growing protoplanet gravitationally attracts ambient nebular gas to form a solar-type atmosphere, which enhances the temperature of the planetary surface more than 2000°K. Assuming that the atmosphere is in convective equilibrium, H. Mizuno and G. W. Wetherill ( Icarus, 1984, 59, 74-86) estimated the dust abundance of the atmosphere and, using a constraint from Ne dissolution, they concluded that the existence of a primary solar-type atmosphere during accretion is not impossible around the proto-Earth. In the present study, conditions for convective stability of the primary atmosphere are obtained; the primary atmosphere is rather convectively stable. In the static radiative atmosphere, the dust abundance, which is determined by a balance between dust production from incoming planetesimals and dust growth by collision, is proportional to (ξ/p s) 1/2 (ξ being efficiency of dust production and ps being sticking probability at collision). New data of Ne dissolution and a moderate mass accretion rate (1 ME/10 7 years, ME being the present Earth's mass) give a more strict condition on the existence of the primary atmosphere than that of Mizuno and Wetherill (1984): the solar-type atmosphere around the proto-Earth should have started escaping at least before the planetary mass was smaller than 0.6 ME.