We present a novel plasmonic antenna geometry - the double resonant antenna (DRA) - that is optimized for second-harmonic generation (SHG). This antenna is based on two gaps coupled to each other so that a resonance at the fundamental and at the doubled frequency is obtained. Furthermore, the proximity of the localized hot spots allows for a coupling and spatial overlap between the two field enhancements at both frequencies. Using such a structure, both the generation of the second-harmonic and its re-emission into the far-field are significantly increased when compared with a standard plasmonic dipole antenna. Such DRA are fabricated in aluminium using electron beam lithography and their linear and nonlinear responses are studied experimentally and theoretically.