The propagation characteristics of doped fiber amplifier have, already, been analyzed using simple coupled-mode analysis (CMA), which steers the interests to apply this simple theory to study the amplification performance of fiber Raman gain amplifier (FRGA). But such study is yet to be done for FRGA. In this paper, a premier report based on CMA is presented to analyze and predict the performance of FRGA for first time, as per our knowledge, using coaxial structure consisting of step-index profiles in both inner and outer cores in terms of effective area, Raman gain coefficient, and effective Raman gain coefficient. In our investigation, we use single pump to compute and compare our results with the results obtained by involved matrix method and a fairly excellent match over a wide region of frequency shift is reported. © 2015 Taylor & Francis.