A nonmean-field model for the ripening of two-dimensional islands is presented. In this model, the adatom sea is divided into many small cells that are the polygons of a Voronoi network. The chemical potentials of adatom seas surrounding different islands are different. Strain generated by lattice mismatch is introduced into the model Computer simulation under periodic boundary conditions is carried out to describe the island ripening in two cases (with and without strain), and demonstrates that small islands may grow faster than large islands, which cannot occur in the mean-field model The simulated results also show that including strain will slow down the evolution of average island size, and an explanation for this is given.