During accretion of the earth by planetesimal impacts, shock degassing of volatile materials occurs, and a proto-atmosphere is formed. Once such an impact-generated atmosphere is formed, the surface temperature of the earth growing by planetesimal impact increases due to the blanketing effect of the atmosphere. We show that the surface of the accreting earth was covered entirely by a ''magma ocean.'' This suggests that the differentiation of the earth proceeds under very low pressure and high temperature conditions during its accretion stage. This places a severe constraint on the amount of volatiles in the mantle, and the formation time of the atmosphere and ocean of the earth.