A mathematical model is developed for the study of free convection film condensation for superheated vapours on a vertical plate. The local film thickness as well as the local heat transfer coefficient (HTC) can be obtained through analytically solving the model. The analytical expression shows that local film thickness is proportional to x(1/4), i.e. delta x=cx(1/4), where c is the only positive solution of a quartic equation, and the expression is similar to the expression of Nusselt's model. The evaluation of thermophysical properties in the film is improved, which could enhance prediction accuracy. Furthermore, the model is validated by Shang and Wang's model, which strictly solved the two-phase boundary equations of vapour and liquid film with consideration of various factors. It is obvious that the proposed model is precise for the prediction of superheated vapour film condensation and convenient for use. In addition, the characteristics of film condensation for water vapour as well as other vapours such as R134a, methane (CH4), nitrogen (N-2), and hydrogen (H-2) are extendedly studied and compared. The results show that variations of heat transfer increase coefficients (HTICs) with subcooling for various vapours have similar trends, but the HTICs are different, e.g. the HTIC for H-2 is 34 times greater than that for water vapour.