For the purpose of obtaining the lower absolute measurement limit of the air kerma in 137Cs ?-ray reference fields, a cavity chamber with a volume of 301.936(19) cm3 was designed and fabricated. The absolute measurement of the air kerma was performed at the minimum effective dose rate of the large-size cavity chamber in our 137Cs ?-ray reference field. With the help of the detailed Monte-Carlo (MC) simulations of the large-size cavity chamber and our 137Cs irradiation facility, the conversion coefficient from the cavity dose to the reference air kerma was calculated. And the obtained air kerma rate with the MC simulation method was 1.429(13) mGy/h. At the same condition, the measured air kerma rates with the cavity theory method and the substitute method were 1.428(13) mGy/h and 1.419(53) mGy/h, respectively. The measurement result with the full MC simulation method agrees with the other two measurement results within 0.07% and 0.70%, respectively. The combination of the large-size chamber and the full MC simulation method can help calibration laboratories achieve the absolute measurement of the low air kerma rate (such as 1.5 mGy/h) in the 137Cs ?-ray reference field.