We propose a bioinspired origami quasi-Yagi helical antenna with beam direction and beamwidth switching capability based on transformable DNA origami structure. Each DNA molecule consists of a double helical chain, and its length can be transformed by folding and unfolding. When three transformable origami DNA structures are applied to the quasi-Yagi helical antenna, beam direction and beamwidth can be controlled by folding and unfolding the origami DNA. The transformable DNA structures act as driven, director and reflector elements. The proposed DNA origami antenna provides four beam direction switching states (three states with narrow beamwidth and one state with wide beamwidth) at fixed frequency of 1.9 GHz. For example, the main beam direction of the proposed antenna can be steered to -30°, 0°, +30° and -40° for states 1, 2, 3 and 4, respectively. State 4 provides a 3-dB wider beamwidth of 104°, whereas the beamwidth of other states is narrower than 64°. The proposed concept is numerically and experimentally demonstrated.