A steering system and method of a mowing vehicle comprise Left and right rear wheels rotating about a king pin for steering the vehicle, an Ackermann steering mechanism for steering these left and right rear wheels and a rear axle housing swingably connected with the vehicle about a yawing axis in a horizontal plane by use of a hydraulic cylinder. When the vehicle makes a U-turn for example to the right during the mowing work, the rear axle housing is fully swung to the left in the horizontal plane by a specified angle and fixed therein while the left and right rear wheels are held at the neutral position. After the rear axle housing is fixed at that angle, the left and right rear wheels are rotated about the king pin to the left and then the vehicle makes a U-turn to the right. When the vehicle finishes to turn, the left and right rear wheels are rotated about the king pin to the right until the neutral position and then the rear axle housing is swung in the horizontal plane back to the right until the neutral position. When the vehicle makes a U-turn to the left, the same operations are carried out. Since the rear wheels are steered after the rear axle housing is swung in the horizontal plane and fixed, the vehicle can make a U-turn with a minimal turning radius, retaining the Ackermann steering condition and the lawn can be prevented from being damaged by the wheels.