A hobbing cutter for manufacturing the isomodulus asymmetric involute gear has a cutting part formed by a segment of Archimedes' worm. The lateral cutting edge of its cutting tooth is on the spiral surface of said worm. The two cutting edges are the intersecting line between the surface of chip flute and lateral relief surface. A positive lead angle and reasonable back-off angles of top and lateral cutting edges are used. Its installation angle is the spiral lead angle.