A filament winding apparatus includes a control unit, a rotation mechanism that rotates a mandrel, a hoop winding head that performs hoop-winding, and a helical winding head that performs helical-winding. The hoop winding head includes bobbins that feed fiber bundles to the mandrel and a circulation mechanism that circulates the bobbins around the mandrel. The control unit controls the rotation and circulation mechanisms such that the mandrel is rotated and the bobbins are circulated in the same direction during helical-winding. It is not necessary to cut fiber bundles after hoop-winding, and wasted fiber is not fed during helical-winding, thereby increasing economy and productivity.