A refrigerator and a driving method thereof are disclosed. A primary compressor(11) and a secondary compressor(12) can form independent cycles together with corresponding evaporators(14,15) so as to reduce unnecessary power consumption. Also, a backflow prevention valve(20) is installed between the primary and secondary compressors to prevent an increase in pressure of the secondary compressor, or an auxiliary heat exchanger(30) is installed at the outlet side of a second evaporator(15) with high temperature to allow heat exchange of an inlet side pipe(L1) of a first evaporator with low temperature so as to shift a load of a freezing chamber into a relatively large refrigerating chamber, thereby improving efficiency of the refrigerator. In addition, an oil separator(120,130) or an oil collection pipe(121,131) is installed at the outlet sides of the compressors or an oil balancing pipe(221) and an oil balancing valve(222) are installed between the compressors, so as to uniformly maintain an oil amount between the compressors.