To design and fabricate a high-speed swept source, we built a short ring cavity based on a fiber Fabry-Perot tunable filter and a semiconductor optical amplifier. First, by on-off control on the semiconductor optical amplifier, a swept laser beam with a duty cycle of 50% was obtained. Then, the beam was subject to staggered superposition after it was divided into two beams by an interleaver, and thus we attained a swept laser beam with a duty cycle of 100% and a swept frequency twice the vibration frequency of the tunable filter. Finally, after re-amplification via a secondary semiconductor optical amplifier, the beam achieved higher power. Specifically, the swept laser beam obtained in this study featured a swept frequency of 245 kHz, a center wavelength of about 1544 nm, a sweep range of 73 nm, an effective coherence length of 12 mm, and average output power of more than 20 mW. In conclusion, the design scheme adopted in this study has important practical significance for the fabrication of a high-speed swept source with high performances and low costs.