The invention provides a fresh-air conditioner and a control method of the fresh-air conditioner. The fresh-air conditioner comprises a conditioner main body, a fresh-air duct, an air exhaust duct, aheat exchanger core body, a fresh-air heat exchanger and an air exhaust heat exchanger, wherein the fresh-air duct and the air exhaust duct are arranged inside the conditioner main body, the heat exchanger core body is arranged inside the conditioner main body, and the fresh-air duct and air exhaust duct respectively pass through the heat exchanger core body, and change heat through the heat exchanger core body; the fresh-air heat exchanger is arranged on the fresh-air duct and is located at the downstream of the heat exchanger core body on the fresh-air duct; and the air exhaust heat exchanger is arranged on the air exhaust duct and is located at the downstream of the heat exchanger core body on the air exhaust duct. The invention reduces the external energy dissipation of the building, and in a green energy-saving building, can not only reduce the indoor cooling/heat production demands, but also reduce the cost of the air conditioner by reducing the volume of two devices and refrigerant quantity, thus solving the technical problem of high power consumption of the fresh-air conditioner in the prior art.