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For many fiber applications, the Brillouin gain spectrum (BGS) contains important information including the Brillouin frequency shift, the Brillouin spontaneous linewidth, and the Brillouin gain coefficient. This paper is the first, to the best of our knowledge, to present an accurate numerical simulation of the BGS in single-mode fibers. The simulated and measured BGS were in good agreement. Through repeated numerical simulations, we revealed a tendency of the peak Brillouin gain coefficient that determines the stimulated Brillouin scattering threshold.