A size-corrected thermodynamic model for clusters is proposed which implies that cluster chemical potential is a linear function of the number of molecules at its surface and the total number of molecules. The model is free from the introduction of the surface tension for small clusters and therefore has no limitation in this size range. The expressions for homogeneous nucleation rates have been obtained in the approximations of small and large critical sizes. Calculated nucleation rates are slightly lower than predicted by the classical theory for water vapor and much higher for mercury vapor, in agreement with the experiments.