In order to solve the problem of poor tuning performence of the optical arbitrary waveform generator based on fiber Bragg grating and piezoelectric transducer, a novel multi-parameter fast tunable Bragg grating filter on lithium niobate crystal was proposed. Theory analysis shows that its Bragg wavelength and corresponding phase is tunable in a linear way with wavelength tuning efficiency of 15.6 pm/V and phase tuning efficiency of 0.2 π/V, and the output light intensity of the filter is controlled by adjusting a polarization rotator also. Simulation results based on transfer matrix theory show that the maximum filtering reflectivity is achieved with the etching duty cycle 1/2, reflectivity more than 98.4% and bandwidth wider than 0.14 nm is obtained when etching depth is deeper than 100 nm on the condition of 10.87 mm grating length, and increasing the wavelength tuning voltage will further reduce the filter bandwidth.