The invention provides a launching catapult launching system and a booster launching method thereof, and belongs to the field of booster devices. The launching catapult launching system comprises a horizontal track, an arc track and a vertical track which are connected in sequence. A rocket is installed on a carrier vehicle. The carrier vehicle runs on the horizontal track, the arc track and the vertical track. Rocket launching can obtain an initial speed by using ground resources, self energy consumption of the rocket can be reduced, and pollution of rocket jetting to the ground environment can be reduced.