The invention discloses an automatic bag-propping and bagging system for woven cone yarn bags and a method of the system. The system comprises a support frame, wherein bag suckers, a bag opening mechanism and a bag propping mechanism are arranged on the support frame in sequence; the bag suckers are connected with the support frame through connecting pieces; the connecting pieces are connected with a first driving mechanism; the bag suckers are arranged above bin positions where the woven cone yarn bags are placed; the bag suckers are used for sucking up the woven cone yarn bags and moving to the bag opening mechanism along the support frame; the bag opening mechanism comprises a second driving mechanism, a roller and rolling wheels; the roller and the rolling wheels are connected with the second driving mechanism, move relatively, and are used for driving the woven cone yarn bags to the bag propping mechanism and opening the mouths of the woven cone yarn bags; and the bag propping mechanism comprises a third driving mechanism; and a lower bag propping sucker and an upper bag propping sucker move downwards and upwards respectively to prop open the woven cone yarn bags, or either of the lower bag propping sucker and the upper bag propping sucker is fixed while the other bag propping sucker moves to prop open the woven cone yarn bags.