A number of models for liquid droplet growth by condensation have been proposed but many of these assume that the supersaturation in the surrounding vapour is small compared to unity. In a number of practical situations, however, this may not be the case and the linear model fails. In this paper we develop a model, based on the general ideas of previous workers, but which is no longer restricted to small supersaturations. Analytical solutions are presented and numerical illustrations are given for the temperature, vapour pressure and saturation ratio at Various distances from the droplet surface. Errors in the droplet growth rate are highlighted when the linear model is used outside of its range of validity: these errors can be significant.