We propose a novel fiber Bragg grating (FBG) sensor interrogation using a Raman-based Fourier-domain mode locking (FDML) fiber laser for a high speed and long distance measurement. A residual Raman pump after the generation of the Raman-based FDML fiber laser is recycled for secondary signal amplification in a 2-m erbium-doped fiber (EDF) to further enhance the output power. The chromatic dispersion is precisely controlled to suppress the phase noise in the FDML laser cavity, resulting in the improvement of an R-number of 1.43 mm/dB. After recycling residual pump, we achieve the 40-km round trip transmission of the sensing probe signal with a high scan rate of 30.8 kHz. With 205-mW residual pump power, the bandwidth and the maximum gain are measured to be more than 50 nm, 10.3 dB at 1550 nm, respectively. The sensitivity of the proposed Raman-based FDML fiber laser to strain is also measured, which are 0.81 pm/μstrain in the spectral domain and 0.19 ns/μstrain in the time domain, respectively.