Fractal regions in a-Ge/Au bilayer thin films after annealing at different temperatures were investigated by TEM, and fractal dimensions were calculated. For 100℃ annealing, un-cleating positions are fewer, large tenuous scale-invariant regions formed with fractal dimension of 1.785±0.01, for 200℃ annealing, uncleating positions increased rapidly, besides thic- ker fractal region with fractal dimension of 1.818±0.008, many isolated island-like regions formed. After 300℃ annealing, only two kind of island-like regions formed with very different size. The relationship between crystallization of a-Ge film, condensation of Au film and mechanism of appearence of fractal region was discussed based on structural and quantitative analyses.