A turbo vacuum pump for compressing a low-pressure gas to discharge the compressed gas into atmosphere comprises pump stator having a gas flow passage comprising a plurality of annular flow passages on an inner surface thereof arranged stepwise diameters of which become smaller toward downstream and passages intercommunicating with adjacent annular flow passages and a gas discharge port communicated with one of the plurality of annular flow passages disposed at the most downstream. The pump stator includes a cylindrical spiral grooved pump impeller and a plurality of peripheral flow pump impellers facing the annular flow passages provided downstream of the cylindrical spiral grooved pump impeller and having stepwise diameters which become smaller toward downstream to form a peripheral flow pump stage. The suction casing has a spiral groove on a cylindrical inner surface thereof arranged with a predetermined clearance in relation to the spiral grooved pump impeller of the pump rotor so as to form a spiral grooved pump stage and a gas suction port communicated with the spiral grooved pump stage.
