A covered wire wrapping tool comprising a covered wire-cutting and cover-stripping device for cutting an elongated continuous covered wire into covered wires of a predetermined length and for stripping covers from a leading and trailing end portions of a severed covered wire, and a wrapping bit device including a single bit having therein an eccentric groove into which the cover-stripped leading and trailing end portions formed by the covered wire-cutting and cover-stripping device are successively loaded. The bit with the cover-stripped leading or trailing end portion loaded in the eccentric groove is rotated to wrap and connect the cover-stripped leading or trailing end portion about and to a terminal of an electrical component.