A homodyne Brillouin optical time-domain reflectometry (BOTDR) based on Raman amplification is proposed to achieve the fast and single-end measurement of temperature and strain in long-range distributed optical sensors. In this method, Raman amplification can be used to enhance multi-Brillouin peaks power in order to improve the power of the Brillouin beat peaks, which can effectively improve the signal-to-noise ratio (SNR) and sensing distance of the sensing system. The co-Raman gain，counter-Raman gain and bidirectional-Raman gain are achieved by solving the coupled equation of the Raman amplification and the power distribution of Brillouin beat peak in front-end Raman pumped system is derived. Take a 50 km large effective area fiber (LEAF) as an example, when the front-end Raman pump power is 800 mW, the lowest SNRs of two Brillouin beat peaks appear at the front end of the LEAF and they are respectively 26.4 dB and 21.5 dB. The SNRs in the rear end of the LEAF are 70.9 dB and 46.8 dB, respectively. The results show that by using the proposed method, the optical fiber sensing dynamic range can be increased by 11 times without degrading the measurement accuracy and speed.