We investigate the efficiency of an optical intensity modulator based on an electrically tunable $LiNbO_3$ reflection grating. Assuming a grating coupling coefficient and the waveguide propagation loss, waveguide length is varied to find its effect on the modulator slope efficiency and the device capacitance. With the low propagation loss of the $LiNbO_3$ waveguide, a very efficient optical intensity modulator can be achieved for a low frequency (${sim}1GHz$) as long as the requirement for the grating coupling coefficient is satisfied.