The phenomenon of water droplet evaporation in hot gaseous flow is investigated numerically in the present study. In the past researches the effects of radiation on the droplet evaporation have not been taken into consideration or only the internal heat generation due to radiation was calculated without considering the droplet evaporation. Since the infrared light, which the droplet in hot environments is subject to, has a wavelength range comparable to the droplet size, the light transverses to heat generated in the droplet. By employing the Mie solution to obtain heat generation inside the droplet, the fluid flow, the heat transfer and the mass transfer inside and outside the droplet are calculated simultaneously. To prove that the numerical algorithm has been correctly applied, the drag coefficient, the Nusselt number and the Sherwood number calculated numerically at steady state are shown to agree well with experimental correlations. To find out the effects of radiation on the droplet evaporation, the water drop at the initial temperature of 300 K and the air of 1,300 K or 1,900 K are employed for case study, and Nu_f and Sh_f are calculated. The higher the gas phase temperature is, the more heat generation occurred inside the droplet. The radiation, however, made no influence on the flow pattern inside the droplet, the transport phenomena, the evaporation, etc., since the imaginary part of the refractive index for water is very small, resulting in negligible heat generation.