The spectroscopic model is proposed to analyze the gain bandwidth of a fiber Raman amplifier (FRA) with a multiple wavelength pumping scheme based on Raman gain theory. The oscillatory lineshape, which is the analytic function to analyze Raman gain spectra, allows us to estimate the gain bandwidth of the FRA. Based on the proposed theoretical modeling, we design and analyze the characteristics of the FRA using the combined multiwavelength pumping sources. We achieved the extended gain bandwidth of the FRA over 80 nm with the small gain ripple less than 0.5 dB. Threshold pumping power and effective noise figure for the FRA can be also analyzed by using the proposed model, which is also applicable for versatile fibers with other doping materials. The proposed analysis method can be useful for the design of FRA with the multiwavelength pumping scheme.