A traveling apparatus suitable for use in a two-wheeled traveling vehicle on which a man rides, and a method for controlling thereof, are provided. An abrupt turn, which can make a rider fall down, is prevented, and stable traveling is obtained without fail. Specifically, the apparatus and method efficiently charge regenerative energy that is generated when decelerating or traveling on a downward slope. The apparatus and method include motors for driving a plurality of wheels independently, a chassis for connecting the plurality of wheels, in which sensors for detecting a shift of barycenter of a rider are provided, and a controller for restricting a rotational velocity of each of the plurality of wheels to a predetermined limited value, wherein turning is performed in accordance with the shift of a barycentric position.