The invention discloses a system and a method for desulphurizing waste gas by cyclic absorption and application thereof. The system comprises a cooling scrubber, an absorbing tower, a lean-rich liquid heat exchanger, a desorbing tower and a reboiler. The system also comprises a purified gas reheater and a demister. The cooling scrubber, the absorbing tower and the demister are connected in sequence; the purified gas reheater is connected with the demister, the reboiler and the cooling scrubber to form a waste gas passage; the absorbing tower is connected with the desorbing tower through the lean-rich liquid heat exchanger to form a desulphurizing liquid loop; and the reboiler is connected with the desorbing tower to form a reboiling liquid and steam loop.