Tunable Fabry-Perot (FP) filters are being increasingly employed in tunable fiber lasers for wavelength selection and tuning. To address single cavity restrictions on transmittivity and achieve narrowband simultaneously, we propose a narrowband tunable electro-optic (EO) filter based on double FP cavities. Lithium niobate (LiNbO3, LN) platform and MgF2 are utilized as film pairs to effectively eliminate the effect of flat-top respond triggered by two cascaded cavities. Thus we can design the FP cavities with a high transmittivity and narrow passband of approximately 99.9% and 0.3 nm, respectively, making it more tolerant to the loss in the cavities. The resonance wavelength around 1550 nm can be blue shifted by 102 nm when the electric voltage is raised from −150 V to 150 V. The error analysis indicates that the incident angle exhibits a certain tuning effect on the wavelength, and the difference between the optical thicknesses of the cavities should be kept to a minimum. The proposed tunable LN filter with double FP cavities may be used in promising applications such as optical communication and photoelectric integration.