We demonstrate that ultra-thin porous alumina membrane (PAM) is suitable for controlling of both size and site of Ge nanodots on Si substrates. Ge nanodots are grown on Si substrates with PAM as a template at different temperatures with molecular beam epitaxy (MBE) method. Ordered Ge nanodot arrays with uniform size and high density are obtained at 400 and 500 oC. Spatial frequency spectrums transformed from scanning electron microscopy images through fast Fourier transform are utilized to analyze surface morphologies of Ge nanodots. The long-range well-ordered Ge nanodot arrays form a duplication of PAM at 400 oC while the hexagonal packed Ge nanodot arrays are complementary with PAM at 500 oC.