The invention discloses an automatic single-drive double-movement bolt tightening device. The device comprises a motor, a speed reducer, a torque sensor, a drive tooth-shaped belt wheel A, a transmission shaft, an electromagnetic clutch, a drive tooth-shaped belt wheel B, an electromagnetic brake, a frame, a tooth-shaped belt A, a ball screw rod spline shaft, a rotation type ball nut component, adriven tooth-shaped belt wheel A, a tooth-shaped belt B, a driven tooth-shaped belt wheel B, a rotation type ball spline sleeve component, a non-contact displacement sensor, a reflection plate, a flange-type ball spline sleeve, a limit ring, a connection component, a compression spring and a spanner component. The automatic single-drive double-movement bolt tightening device is single-drive, full-automatic, high in efficiency, compact in structure, and suitable for being used on an automatic production line. The automatic single-drive double-movement bolt tightening device has the coupling ability, has wide application range, and can be used for tightening bolts with different screw pitches. The invention further provides a bolt tightening method of the automatic single-drive double-movement bolt tightening device.