The invention relates to an inerting system with a nitrogen-rich gas storage function. The inerting system comprises an air separator, a nitrogen-rich gas storage tank, a first stop valve, a second stop valve, a third stop valve, a fourth stop valve, an oxygen concentration sensor, a pressure sensor and an inerting controller. In the climbing and cruising stages of an airplane, when it is measured that the oxygen concentration in a fuel tank is within a safe range, the inerting controller controls the first stop valve and the third stop valve to be opened and controls the second stop valve and the fourth stop valve to be closed, and the air separator supplies nitrogen-rich gas to the gas storage tank; and in the descending stage of the airplane, when it is measured that the oxygen concentration in the fuel tank exceeds the safety range, the inerting controller controls the first stop valve, the second stop valve and the fourth stop valve to be opened and controls the third stop valve to be closed, and the air separator and the air storage tank supply nitrogen-rich gas to the fuel tank at the same time. According to the technical scheme, the system has the following beneficial technical effects that the nitrogen-rich gas can be reasonably and efficiently distributed to the target fuel tank, and the low oxygen concentration state in the fuel tank in the descending stage is kept.