A new optical frequency shifter that can shift the light frequency in the microwave or millimeter-wave frequency range is presented. It is based on the use of stimulated Brillouin scattering gain and loss spectrums in an optical fiber to suppress one sideband of a double-sideband suppressed carrier modulation signal while amplifying the other sideband. The new optical frequency shifter only involves optical components and is capable of operating over a wide frequency range with low spurious generation and with tunable capabilities. It can be also used as a single-sideband suppressed carrier modulator. Experimental results demonstrate a 20 GHz frequency shift with a 25 dB signal-to-noise ratio and a widely tunable frequency shifting operation. © 2009-2012 IEEE.