A new approach to the estimation of erythemally effective ultraviolet (EUV) radiation for all sky conditions that occur in maritime Antarctica is reported. The spatial variability of the total ozone content (TOC) and attenuation of the EUV radiation in the atmosphere are taken into consideration. The proposed nonlinear regression model of EUV radiation is described by a hyperbolic transmission function. The first results and the model validation for Vernadsky Station (formerly the British Faraday Station) during the period 2002–2005 show very good agreement with the measured values (R = 99.2). The developed model was evaluated using daily doses of EUV radiation with respect to solar elevation angle and cloudiness. The mean average prediction error (MAPE) for cloudy (4.1–7.0 oktas) and overcast skies (7.1–8.0 oktas) varied between 4.0% and 4.3%, while for partly cloudy days (0–4.0 oktas) with high variability of cloud types during a day, MAPE reached 5.9%.