Single sideband modulation output is demonstrated by using of the fiber Bragg grating (FBG) and the Mach-Zehnder electro-optic modulator. Based on the microwave-sweeping single sideband modulation technique, a method to measure the characteristics of the fiber stimulated Brillouin scattering (SBS) is proposed. It can be used to measure the Brillouin frequency shift together with the Brillouin gain spectrum effectively. The properties of the stimulated Brillouin scattering in a 50 m photonic crystal fiber are measured, where the Brillouin frequency shift is 9.7443 GHz, the linewidth of the Brillouin gain spectrum is 22.472 MHz, and the Brillouin gain coefficient is 7.874×10-12 m/W, respectively.