We demonstrate that the single-layer graphene film can be directly grown on semiconductor SiGe substrate by using ambient pressure chemical vapor deposition. It is apparent that SiGe has a very strong catalytic ability for direct fabrication of high-quality graphene film. In comparison with various transition metal-based catalysts, this strategy can utilize the standard equipment available in semiconductor technology which is of maturity and is scalable. The crystallinity and thickness were investigated using Raman spectroscopy, scanning tunneling microscopy and transmission electron microscopy. The field-effect transistors were fabricated and characterized to determine the electrical properties of the synthesized graphene film. Moreover, this formation method of graphene-on-SiGe junction enables us to fabricate electronic devices based on this structure in microelectronics and optoelectronics.