Variation-correlation function (VCF)I a fractal model for quantitative analysis on 3D surface, has been applied to the description of Go-based thin film surfaces imaged by atomic force microscope (AFM). The results of two group experiments on the thin films have implied that the change in fractal dimension D-cor is in accordance with that in surface energy E-sv of the thin films but height roughness Ra and Rms are not. A theoretical equation has been developed to demonstrate the relationship between fractal dimension D-cor and surface energy E-sv. This equation shows that D-cor can be interpreted as a parameter of surface energy in thin film growth and thus the thin film surfaces have fractal nature. This equation also successfully explains the phenomenon of fractal dimension decrease for the thin films during annealing. This study shows that VCF method provides a reasonable parameter for quantitative description of irregularity of thin film surfaces.