This letter presents experimental results concerning a thin film bulk acoustic wave resonator realized on a thin GaN membrane and covered with a thin film of double walled carbon nanotube mixture. The quality factor was measured before and after the coating of the resonator with the nanotube thin film. The quality factor has increased more than ten times when the resonator was coated with nanotubes, due to their high elasticity modulus and low density, which confers a much higher acoustic impedance of the resonator electrodes and thus confines much better the longitudinal acoustic standing waves inside the resonator.