A gamma-ray source with an intense component around the giant dipole resonance for photonuclear absorption has been obtained via bremsstrahlung of electron bunches driven by a 10-TW tabletop laser. 3D particle-in-cell simulation proves the achievement of a nonlinear regime leading to efficient acceleration of several sequential electron bunches per each laser pulse. The rate of the gamma-ray yield in the giant dipole resonance region (8 < E(gamma)< 17.5 MeV) was measured, through the radio activation of a gold sample, to be 4x10(8) photons per joule of laser energy. This novel all-optical, compact, and efficient electron-gamma source is suitable for photonuclear studies and medical uses.