In recent years, the amount of energy consumed by data centers has tended to increase. Therefore, power savings are strongly suggested. Data centers must be cooled yearround due to the extremely large amount of heat emitted from the IT devices. Therefore, to decrease year-round energy consumption, it is important to use low-temperature outdoor air during cool seasons such as mid-to-late fall and early spring and cold seasons like winter. Thus, we investigated cooling systems that use low-temperature outdoor air, and we developed a package air conditioner (A/C) that has cooling functions that use outdoor air. The new A/C combines a compression cycle and a cycle that stops the compressor and circulates coolant with a pump; it operates by switching to a compression cycle when the outdoor temperature is high and switching to a pump cycle when the outdoor temperature is low. Specifically, the pump cycle is the system of taking the low-temperature outdoor air into a coolant cycle from the heat exchanger in the outdoor unit (indirect outdoor-air cooling method) and transporting cold energy into the room with a pump. The A/C reduces the energy consumption in low outdoor temperatures by operating in favor of the efficient pump cycle. In this report, in order to verify the characteristics of the A/C, we built a simulation mathematical model. In addition, we verified the validity of the mathematical model compared to the measured value of the prototype. We show the effects of refrigerant circulation and outdoor-air temperature as an example of the verification simulation using a mathematical model.We calculated the annual energy consumption of the package A/Cs with refrigeration pumps based on the outdoor-air temperature data and the operating efficiency of the outdoor-air temperature. Specifically, the A/C that we developed reduced energy consumption by 50% in New York and 53% in Chicago, compared to the energy consumption of conventional computer-room A/Cs.