A new optical frequency shifter is presented. It is based on a double sideband suppressed carrier radio-frequency (RF) modulated optical signal into a Brillouin-assisted filter, which is formed by a Brillouin medium between a pair of optical circulators. The frequency shifting operation is realized by utilizing multiple stimulated Brillouin scattering gain and loss spectra to amplify one of the third-order sidebands but attenuate the other sidebands. The frequency shifter has a simple structure and a high frequency shifted to unwanted frequency component ratio. It also has the ability to realize a very large frequency shift, which is three times the input electrical driving signal frequency. The frequency shifter is experimentally demonstrated with the results showing a 32.53 GHz optical frequency shift of a continuous wave light at 1551.016 nm with over 34 dB difference between the wanted frequency shifted and unwanted frequency components.