A rear air conditioner for a vehicle including a discharge module mounted at an air outflow port of an air-conditioning case and having a discharge case and a rotary mode door; two face vents formed at both side walls of the discharge case; a floor vent formed at the center of the discharge case; and an air mixing zone formed inside the rotary mode door, thereby reducing the size of the air conditioner because a plurality of the vents are intensively arranged in the discharge case, enhancing installability due to the modulated components, reducing a temperature difference of the air discharged to the left and right sides inside the vehicle due to an improved mixability. The inside of the rotary mode door can be utilized as the air mixing zone. The degrees of opening of the face vents and the floor vent are controlled by the single mode door.