The present invention provides a gearshift overlap control system and a control method for improving vehicle dynamic response; the control system includes a gearshift progress calculation module: the gearshift progress calculation module is capable of calculating a gearshift progress in real time; a clutch control module: the clutch control module is capable of executing a first power-on downshift control and starting to perform a second power-on downshift control when a set second power-on downshift in a corresponding gearshift progress is requested; and an iterative learning control module: the iterative learning control module is capable of automatically adjusting a first on-coming clutch control pressure and a first off-going clutch control pressure in the first power-on downshift by means of monitoring the overshoot of the gearshift progress.