With the rapid increase of the output power of fiber lasers, the stimulated Raman scattering effect in optical fibers has also attracted more and more attention. On the one hand, it is one of the main limiting factors for the further increase in the power of current high-power fiber lasers. On the other hand, it can be used as a new way for laser generation, which is expected to achieve both high-power and wide-band laser output. Current Raman fiber lasers are mainly based on low-loss quartz fibers. In order to optimize the performance of a Raman fiber laser, the researchers doped the quartz fiber with different elements to change its Raman response characteristics. For example, the Raman gain coefficient of optical fibers can be increased by doping germanium, and the Raman peak with a frequency shift of about 40 THz can be introduced by doping phosphorus elements to achieve wavelength conversion with a large frequency shift. Different doping components and doping concentrations will change the Raman gain spectrum of the fiber, and the measurement of Raman gain spectrum of the fiber is of great significance for the design of Raman fiber lasers. Currently, the measurement of the Raman gain spectrum of optical fiber is mainly based on the small signal method, which has a long testing time, and the measurable frequency shift range is limited by the wavelength tuning range of the seed laser, so it is difficult to obtain the Raman gain spectrum of the fiber over broad frequency shift range.To measure Raman gain spectrum of the fiber over broad frequency shift range, a new method which derive the Raman gain spectrum of optical fiber from its spontaneous Raman scattering spectrum is proposed. Firstly, the backward Raman scattering spectrum is measured by the experimental setup (Fig.7). The pump source is a ytterbium-doped fiber laser operating at 1018.4 nm. Two bandpass filters are spliced after the pump source to remove the background noise. The filtered pump is coupled into the test fiber through a circulator. And the backward Raman scattered light is transported into the optical spectrum analyzer through the P2-P3 passage of the circulator. The backward Raman scattering spectrum of the test fiber can be obtained by subtracting the transmission spectrum of the P2-P3 passage (Fig.2(b)) from the output spectrum from P3 port of the circulator. Secondly, the Raman output powers under different Raman gains is calculated using the power balanced model. From the measured spontaneous Raman scattering spectrum and the calculated Raman output powers at different Raman gain coefficients, the Raman gain spectrum of the test fiber can be obtained.The simulated Raman output powers at different Raman gain coefficients is shown (Fig.5(b)). The output spectrum from P3 port of the circulator is shown in Fig.8(a). From the data above, the Raman gain spectra of a phosphorus-doped fiber and germanium-doped fiber over a broad frequency shift range of 1-42 THz are obtained. The measured results are shown (Fig.8(b)). To validify the accuracy of this method, the measured Raman gain coefficients are compared to that measured by the traditional small signal amplification method. In the frequency shift range of 1.6-22 THz, the results agree well with the Raman gain data measured by the traditional small signal amplification method.A new method to derive the Raman gain spectrum of optical fiber from the spontaneous Raman scattering spectrum is proposed. Using this method, the continuous Raman gain spectra of a phosphorus-doped fiber and an undoped silicon-based fiber in the range of 1-42 THz are obtained. In the range of 1.6-22 THz, the Raman gain coefficients obtained by this method agrees well with the results of the small signal amplification method. This work provides a convenient and accurate method for measuring the continuous fiber Raman gain spectrum over broad frequency shift range.