If the Earth was formed in a stage before the gas of a solar nebula was dissipated, it was surrounded by a dense primitive atmosphere with the solar chemical composition. The atmosphere was gravitationally bound to the Earth after the solar nebula was dissipated by strong solar wind in a T Tauri stage. We calculate numerically the escape of this atmosphere due to heating by strong solar radiation, especially by far-UV radiation absorbed through photodissociation of water molecules. We assume that the flow of the atmospheric gas is spherically-symmetric and steady. The results show that the efficiency of mass loss by the far-UV radiation is very large compared with the case of EUV radiation, which was studied previously, and that the atmosphere was wholly dissipated within 2×10^7y, i.e., a typical period of the T Tauri stage, if the far-UV flux was more than 1×10^2 times as large as the present value. This flux is well expected from observations of T Tauri stars. The effect of solar wind is found to be unimportant.