CO_2 is recognized as one of the most suitable natural working fluid for compression heat pump to heat cold water to hot temperature region. But the coefficient of performance (COP) for cooling is not high. This is because the temperature of the working fluid discharged from compressor is so high to the heat sink that is often the outside air temperature. When a low temperature heat sink is available, cooling for the air conditioning by CO_2 heat pump can be realized. In this study, river water, underground water and ground are supposed as heat sink. When the low temperature heat sink is used and expansion at 25 C is realized, cooling COP is improved and shows the value 5.89 for single stage compression and 6.67 for two stage compression with flash cycle. These values are very close to those obtained by the conventional system that uses R410A.