We report a new electrooptic traveling-phase grating with periodic domain inversion and its application to ultrafast unidirectional beam deflection. The electrooptic traveling phase grating utilizes Raman-Nath diffraction to spatially separate input light to many diffracted beams on the far-field plane. Then, unidirectional optical beam deflection can be achieved by adjusting amplitudes and phases of the diffracted beams. In the experiment, ultrafast unidirectional deflection by the traveling phase grating is demonstrated at 16.25 GHz using a simple phase-only control.