A tunable long-period waveguide grating coupler based on LiNbO3 was proposed. The light can be coupled effectively from the input waveguide to output waveguide through the cladding because of the long period gratings′ unique feature. The effective refractive indexes of the core and cladding of the waveguide grating will change accordingly as a result of electro-optic effect when a tunable voltage is applied, making the resonance wavelength and the coupling efficiency tuned by controlling the applied tuning voltage. The effects of coupler length and the grating period on bandwidth and the coupling efficiency tuning range, and the influence of the waveguide size on the resonant wavelength tuning sensitivity were analyzed. The results show that the shorter grating period and the greater coupler length lead to the narrower bandwith and the greater coupling efficiency tuning range. In addition, the resonance wavelength tuning sensitivity decreases with the increase of waveguide width, and the influence of thickness on the resonance wavelength tuning sensitivity can be ignored. For the coupler with the grating period of 94 μm and the coupler length of 3.52 cm, the simulation results show that the resonance wavelength tuning sensitivity can reach 26.2 pm/V, and the bandwith of 3 dB as 4.5 nm, when the applied voltage varying from 0 to 200 V, the resonant wavelength change 5.24nm, and the coupling efficiency can be tuning from 1 to 0.15.