We report a kind of electric field tunable transparent and flexible capacitor with the structure of graphene-Bi1.5MgNb1.5O7 (BMN)-graphene. The graphene films with low sheet resistance were grown by chemical vapor deposition. The BMN thin films were fabricated on graphene by using laser molecular beam epitaxy technology. Compared to BMN films grown on Au, the samples on graphene substrates show better quality in terms of crystallinity, surface morphology, leakage current, and loss tangent. By transferring another graphene layer, we fabricated flexible and transparent capacitors with the structure of graphene-BMN-graphene. The capacitors show a large dielectric constant of 113 with high dielectric tunability of ~40.7 % at a bias field of 1.0 MV/cm. Also, the capacitor can work stably in the high bending condition with curvature radii as low as 10 mm. This flexible film capacitor has a high optical transparency of ~90 % in the visible light region, demonstrating their potential application for a wide range of flexible electronic devices.Electronic supplementary materialThe online version of this article (doi:10.1186/s11671-015-0974-4) contains supplementary material, which is available to authorized users.