Frequency sweeping optical source (FSOS) is widely used in optical communications, optical sensing and optical imaging. Sweeping span and sweeping speed of the FSOS is critical to its performance. A new method to broaden the sweeping span and accelerate the sweeping speed of the FSOS is proposed. Single sideband modulation is adopted in a recirculating frequency shifter to enhance the frequency sweeping electric-optic modulation and generate stable high-order optical comb. So a wider optical frequency sweeping span is obtained with narrow-band electrical sweeping signal given the identical linearity and narrow linewidth. An optical frequency sweeping span of 11.44 GHz is obtained by radio frequency sweeping span of 200 MHz, the frequency is broadened approximately by 57 times. Meanwhile, the frequency sweeping speed is improved by 57 times as each sweeping period remains not changed.