An optically tunable frequency-doubling microwave generation technique based on stimulated Brillouin scattering (SBS) in optical fibers is proposed and experimentally demonstrated. Due to the strong dispersion characteristics in SBS, when a up/2 phase shift is imposed on the optical carrier of an amplitude-modulated signal by SBS, only a frequency-doubling microwave signal from the beating between the optical carrier and the 1st sidebands is generated. Due to the inherent narrowband character of SBS and the phase shift being only imported on to the optical carrier while the sidebands are kept unchanged, the frequency-doubling with large frequency tunability is realized, the operational bandwidth is just limited by other optical device deployed. In addition, all the required optical signals and pumps can be generated from the same laser source, the influence from the wavelength drifting is eliminated, so the stability of the system is established.