We propose an electro-optic on-chip beam shifting device based on gradient microstructured electrodes and an optical tapered waveguide fabricated using lithium niobate (LN). The distribution of refractive index variations of the optical waveguide can be electro-optically defined and tailored by the designed gradient microstructured electrodes, which directs the beam propagation and shifting. The length of the beam shifting device is 18 mm and the width of the waveguide is gradually increased from 8 μm to 80 μm. The functionality of the beam shifting device is experimentally demonstrated, and it is observed that it has an electro-optic tunability of 0.41 μm/V, and a high-speed response time of 19 ns (λ=1310 nm). This study can provide potential applications in optical switching and modulation, beam scanning and ranging, optical spatial communications, etc.