Molecular beam epitaxy growth of an InxGa1-xAs/GaAs quantum well(QW) structure(x equals to0.17 or0.3) on offcut(100) Ge substrate has been investigated. The samples were characterized by atomic force microscopy, photoluminescence(PL), and high resolution transmission electron microscopy. High temperature annealing of the Ge substrate is necessary to grow GaAs buffer layer without anti-phase domains. During the subsequent growth of the GaAs buffer layer and an InxGa1-xAs/GaAs QW structure, temperature plays a key role. The mechanism by which temperature influences the material quality is discussed. High quality InxGa1-xAs/GaAs QW structure samples on Ge substrate with high PL intensity, narrow PL linewidth and flat surface morphology have been achieved by optimizing growth temperatures. Our results show promising device applications for III- V compound semiconductor materials grown on Ge substrates.?2011 Chinese Institute of Electronics.