The invention provides a torsional vibration prevention connection structure and a torsional vibration prevention hollow rotor structure. The torsional vibration prevention connection structure comprises a first connection member and a second connection member used for respectively connecting different shafts, and an elastic member capable of delivering torques. The elastic member is connected between the first connection member and the second connection member. The torsional vibration prevention connection structure can prevent the torsional vibration, and can prevent the torsional vibration of a spindle system connection or a single spindle, thereby ensuring the stability of the spindle system and the single spindle.