The invention relates to an internal overlapping refrigerator system with an air supplementing compressor and a control method. By means of the system, a binary non-azeotropic mixing working medium isadopted, a gas-liquid separator is used for achieving separation of high and low boiling point working media, it is guaranteed that more low boiling point working media enter a refrigeration evaporator, the air suction pressure of the compressor is improved, and the power dissipation of the compressor is reduced; the air supplementing compressor is used in the refrigerator system, the exhaust gastemperature of the compressor can be effectively reduced, the efficiency and reliability of the compressor are improved, in addition, by using the air supplementing compressor, the irreversible heattransfer loss of the refrigerator evaporator can be greatly reduced, and the system energy consumption is further reduced; a traditional refrigerator system has the shortcomings that the compressor pressure is large, the exhaust gas temperature is high, and the energy efficiency is low, the internal overlapping refrigerator system uses the air supplementing compressor and the internal overlappingtechnology, the problems can be effectively solved; and the invention further provides a feasible and effective control method, and therefore the system is guaranteed to run efficiently and reliably all the like.