In this study, Cu thin films with layer thicknesses of 5, 25, and 50 nm were prepared by DC magnetron-sputtering method and their three dimensional (3-D) surface topography were investigated. Concretely, the 3-D surface roughness of samples was studied by atomic force microscopy (AFM), fractal analysis of the 3-D AFM-images and power spectral density (PSD) function. Also the content of thin films was characterized by X-ray diffraction (XRD). The thin films were prepared onto glass and p-type silicon (100) substrates by DC magnetron-sputtering method and were studied over square areas of 4.4 μm × 4.4 μm using AFM and fractal analysis. The 3-D surface morphology revealed the fractal geometry of Cu thin films at nanometer scale, which can be quantitatively estimated by the fractal dimension D_f that was determined by cube counting method, based on the linear interpolation type. The results from AFM data indicated the possible presence of superstructures on the growth process of Cu nanostructures that were in relatively good agreement with XRD data and PSD.