The invention provides a cylinder driving type digital controlled lathe tailstock automatic feeding control method capable of achieving floating tapping. A digital controlled lathe saddle and tailstock engaging and disengaging connecting device is adopted and comprises a connecting pillar, a rotating arm component, a driving component and a screw tap component, wherein a ring slot is formed in the middle of the connecting pillar, and a pair of sensors are arranged at the shaft end of the connecting pillar and on the side face of a tailstock; the rotating arm component comprises a rotating arm, a rotating shaft, a shaft sleeve and a big gear, and the shaft sleeve is fixed to the front side face of the digital controlled lathe tailstock; the rotating shaft penetrates through the shaft sleeve, the front end of the rotating shaft is fixedly connected with the rotating arm, the other end of the rotating shaft is fixedly connected with the big gear, and a hook part capable of being clamped into the ring slot is arranged at the front end of the rotating arm; the driving component comprises a rack, a cylinder, an electromagnetic directional valve, a rack guiding groove, a reset switch and a controller, the controller is installed in a machine tool power distribution cabinet and electrically connected with a digital control system and the electromagnetic directional valve, and the reset switch is installed on the front side of a digital controlled lathe saddle and electrically connected with the controller.