Quasars are essential for astrometric in the sense that they are spatial stationary because of their large distance from the Sun. The European Space Agency (ESA) space astrometric satellite Gaia is scanning the whole sky with unprecedented accuracy up to a few uas level. However, Gaia's two fields of view observations strategy may introduce a parallax bias in the Gaia catalog. Since it presents no significant parallax, quasar is perfect nature object to detect such bias. More importantly, quasars can be used to construct a Celestial Reference Frame in the optical wavelengths in Gaia mission. In this paper, we compile the most reliable quasars existing in literatures.The final compilation (designated as Known Quasars Catalog for Gaia mission, KQCG) contains 1842076 objects, among of them, 797632 objects are found in Gaia DR1 after cross-identifications. This catalog will be very useful in Gaia mission.