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 year-round 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.