Donor doping can increase the dielectric constant of a material by several orders of magnitude due to induced space charge causing interfacial polarization. Giant dielectric properties and interface polarization are also both expected to greatly enhance the flexoelectric behavior of a material. In this work, a typical flexoelectric ceramic material, BaTiO3, was selected and donor doped using elemental Nb. Compared with the nominal BaTiO3 ceramic, the dielectric constant and flexoelectric coefficient of the Nb-doped BaTiO3 ceramics were significantly improved. The transverse flexoelectric coefficient of 0.3 mol. % Nb-BaTiO3 was found to increase to nearly 40 times the nominal value, reaching 387 μC/m. The results indicate that the giant dielectric response, and therefore the giant flexoelectric response, is the result of the combined effects of internal barrier-layer capacitance and surface barrier-layer capacitance. This study not only deepens the understanding of the semiconductor macro-dielectric effect and the flexoelectric mechanism caused by doping, but it also provides a feasible strategy for the design of giant dielectric/flexoelectric response materials and related devices with high dielectric constants and flexoelectric coefficients.