The present disclosure relates to a stabbing system for installing an offshore jacket structure and an installation method for installing an offshore jacket structure using the same. Particularly, the stabbing system fixes, to a seabed-pile, a jacket leg of a jacket structure to be inserted into the seabed-pile that was pre-inserted into the seabed and includes: a stabbing member that is installed on an external surface of the jacket leg and supported by an upper end surface of the seabed-pile when the jacket leg has been inserted into the seabed-pile; a vertical gripper that is installed in plural number in the stabbing member and operated toward an upper end surface of the seabed-pile to adjust a horizontality degree of the jacket leg; a horizontal gripper that is installed in plural number in the outer periphery of the stabbing member and operated toward an external surface of the seabed-pile to fix the jacket leg to the seabed-pile; and a grouting unit that introduces grout into a space between the jacket leg and the seabed-pile, in a state that the jacket leg has been fixed inside the seabed-pile.