A rear air conditioner for a vehicle is provided to introduce a maximum amount of hot air passing through a heater core via a floor outlet and introduce cold air via a vent outlet for discharging the hot air to leg parts of passengers and the cold air to head parts of the passengers in a mixing mode, thereby improving pleasant feeling of the passengers. A rear air conditioner for a vehicle includes a floor outlet(140) formed at an upper part of a heater core(400) and adjacent to a rear path of the heater core. An air induction element is mounted in the rear path for inducing air passing through the heater core toward the floor outlet. The air induction element is a vertical stepped part(123) formed at a case(100) with a stepped difference in the right and left directions for increasing an area of a path(121) adjacent to the floor outlet becomes wider than that of a path(122) remote from the floor outlet in the rear path.
