Raman spectroscopy is an important technique for analyzing the chemical composition of samples in many fields. A severe challenge often encountered in Raman measurements is the presence of a concurrent fluorescence background, especially in biological samples. In order to obtain accurate Raman spectra, the fluorescence background must be subtracted from the original Raman spectra. We proposed a shifted ratio spectrum method to subtract the strong fluorescence background from the original Raman spectrum. First, the original Raman spectrum is divided into multiple regions according to the spectral shape of the shifted ratio spectra, and then, Gaussian fitting is performed in each region. The fitting results are stitched together in order to obtain the complete fluorescence background. Finally, this fluorescence background is subtracted from the original spectrum to obtain a pure Raman spectrum. This method can accurately subtract the fluorescence background of Rhodamine 6G (R6G)/ethanol solution and serum. This highlights the great potential of this method for applications in both biological and non-biological samples.