Tunable optical wavelength filters are indispensable components in optical communication systems. In this paper, an ultra-narrowband tunable filter inscribed in lithium niobate (LN) wafer is designed. Two sections of Bragg grating and a pair of electrodes are fabricated in the LN waveguide. The operation wavelength could be tuned by adjusting the electric voltage applied on the electrode pair owing to the electro-optic effect of LN crystal. Simulation results indicate that the filtering bandwidth of the proposed phase-shifted Bragg grating is determined by grating lengths no longer than 1 pm. The tuning sensitivity is dependent on the distance between the two gratings. In addition, the proposed structure overcomes the difficulty in controlling the phase shift of the grating pair, ensuring its potential applications in optical sensing systems.