The Finite Difference Time Domain (FDTD) method is used to adjust the interval period multilayer structure of the narrow band-stop filter in mid-infrared of graphene nanometer film and refractive index regulable lithium niobate (LiNbO3). First, it is necessary to control the number of layers for the multilayer structure to adjust the filter characteristics. The numerical result shows that with the increase of the layer number, the transmission rate decreases, the wavelength corresponding to the minimum transmittance is shortened, the width of the band-stop significantly narrows down, and the narrow-band characteristics curve gets very sharp. Second, a change in the chemical potential of the dielectric constant for each layer of graphene by adjusting the voltage to achieve the adjustment of the narrow-band filter characteristics is necessary. The numerical result shows that for the same number of layers, the wavelength corresponding to the minimum transmission rate is shortened with the increase of the chemical potential. When there are more layers, the minimum transmission rate changes in the short wavelength; when there are few layers, the minimum transmission rate changes in the long wavelength. Third, a change in the refractive index of the lithium niobite (LiNbO3) crystal in the multilayer structure through voltage changes to achieve the adjustment of narrow-band filter characteristics, is also necessary. The numerical results show that for the same number of layers, the wavelength corresponding to the minimum transmission rate gets longer with the increase of the refractive index of the lithium niobite (LiNbO3) crystal. When there are more layers, the minimum transmission rate changes are in the short wavelength; when there are few layers, the minimum transmission rate changes are in the long wavelength.