Using atomic force microscopy (AFM), the kinetic surface roughening in electrochemical dissolution of nickel films at a low constant current density was studied in order to reveal the scaling laws. The surface measurements of AFM exhibited the oscillatory variation of the interface width with time, which made it impossible to determine the growth exponent beta. The oscillatory behavior of surface roughening was explained by the presence of unstable passive films formed on the nickel film surface. The roughness exponent alpha=0.94 +/- 0.04 calculated from the AFM images of the anodic dissolved surface was almost equal to that predicted by the diffusion-driven growth model.