The invention relates to a flexible driving connecting mechanism. The flexible driving connecting mechanism comprises a motor installation case; a speed reducer and a motor are installed on the motor installation case; a power output shaft of the speed reducer extends out of the lower portion of the motor installation case; a gear bush is sleeved on the power output shaft of the speed reducer; a bearing is installed between the gear bush and the motor installation case; a driving gear is arranged on the end portion of the gear bush. The flexible driving connecting mechanism is characterized in that a long bolt is arranged on a lateral plate which is arranged on one side of the motor installation case; one end of the long bolt is fixed on a machine tool through nuts; the other end of the long bolt is provided with a pressure pad; a pressure spring is arranged between the pressure pad and the lateral plate of the motor installation case; the other side of the motor installation case is sleeved on a rotary shaft which is installed on a support; a bushing is sleeved on the rotary shaft. According to the flexible driving connecting mechanism, the motor installation case can rotate around the rotary shaft to form into backlash compensation through flexible adjustment of the pressure spring, flexible adjustment of transmission gap during the transmission process is achieved, and operation of the machine tool is stable.