The present invention provides a wing-flapping flying apparatus, which can fly by moving its wings similar to a bird hovering or flying in the air by flapping its wings. The wing-flapping flying apparatus comprises: a body; a rotating shaft rotatably joined to the body; driving means for rotating the rotating shaft; and wings reciprocated between two points and connected to the rotating shaft so as to be rotated together with the rotating shaft and to be relatively torsionally rotated with respect to the rotating shaft. The wing-flapping flying apparatus generates lift throughout an entire wing-flapping movement without generating lift only throughout the half of a wing-flapping movement or offsetting the generated lift by the other half of the wing-flapping movement. Therefore, the wing-flapping flying apparatus can provide not only a stable flight but also a softly hovering or ascending and descending flight.