The initial heteroepitaxial growth stages of GaAs on Ge(100) by all-solid-source molecular beam epitaxy(MBE) were studied by means of reflection high-energy electron diffraction (RHEED), high resolution X-ray diffraction (XRD) and atomic force microscopy, as well as the effects of different growth conditions to the epitaxial layer qualities. It was indicated that high growth temperatures or low growth rates enabled a layer-by-layer growth mode of initial GaAs nucleation layer which was evidenced by RHEED patterns. However, the combination of low growth temperatures and low growth rates for the initial GaAs layer gave lower full-width at half-maximum value of rocking curves and lower surface roughness of the epitaxial materials, owing to the decrease of the lattice mismatch between substrates and epi-layers.