With the introduction of overlapping factor, a new simulation model for fiber Raman amplifiers (FRA) is proposed. Using this new model in FRA simulation leads to obvious reduction of iteraction time with satisfactory accuracy. The effect of dispersion and nonlinearity on super Gaussian pulse pumped Raman amplifiers has been studied by solving the new model. The simulating results show that dispersion has great impact on the performance of fiber Raman amplifiers, while nonlinearity make little influence on in.