Silver nanostructures are of interest to be used in hybrid thin-film structures with various materials. In this work, we analyse 3D AFM images of granulated silver film nanostructures prepared by thermal evaporation. The advanced AFM data study aims to understand how film thickness and postannealing affect the nanostructure morphology changes. For the first time, the evaluation of surface statistical parameters and fractal geometry were used to characterise the nanostructure morphology of Ag island films. The samples with gravimetric thickness of 2, 4 and 10 nm were analysed before and after annealing at 200°C for 10 min. The statistical processing revealed the essential variation of parameters with Ag film thickness increment and as a postannealing result. The nonmonotonic variation of surface roughness, skewness and fractal dimensions were found. It is caused by the features of the film growth process with the thickness increment and thermally activated diffusion of Ag nanoparticles during annealing.