A novel numerical method for fiber Raman amplifier (FRA) from standard propagation equations is presented and derived based on the one-step method for ordinary differential equation (ODE). The proposed algorithm is effective in solving FRA equations including all the interactions among pumps, signals, and noises. Applications of the numerical analysis to practical FRA-based systems show a great reduction in computation time in comparison with the average power method and the fourth-order Runge-Kutta (RK) method, under the same condition. Also the proposed method can decrease the computing time over three orders of magnitude with excellent accuracy promises in comparison with the direct integration method.