Silicon photonics is considered as a promising technology to realize high-performance photonic integrated circuits, owing to its complementary metal oxide semiconductor-compatibility which is applicable for large-scale integration at low cost. However, due to the limitation of optoelectronic properties of silicon, the challenge to the realization of high-performance active device on the silicon integrated platform still exists. The recent development of graphene-silicon hybrid photonic integrated circuit provides a practical solution to this problem, because graphene, as a superior two-dimensional material, possesses many advantageous optoelectronic properties, such as high mobility, high electro-optical coefficient, and broadband absorption, which can be fully exploited to break through the material limitation of silicon. Moreover, compared with other active integrated materials such as germanium and compound semiconductors, graphene is cost-effective and can be conveniently integrated with silicon photonic device. Here, we review some important research progress of graphene-silicon hybrid photonic integrated circuits that include optical sources, optical waveguides, optical modulators, and photodetectors. The challenges and prospects of these devices are also analyzed, which are expected to be beneficial to the relevant research communities.