We report the transmission of signal light and the noise accumulation in the fiber Raman amplifier (FRA) under four-wavelength time-division multiplexing (TDM) pumping. A quality factor that is used to describe the performance of the Raman fiber amplifier system in quantitative analysis is proposed. The results indicate that the power variation of signal light has a certain periodicity that is related to the period of pumping with the TDM pumping. The shorter the pumping period is, the weaker the signal fluctuation is. Through the analysis of noise, it is found that amplified spontaneous emission is the main source of the noise of FRA with TDM-pumping. By comparing the TDM pump scheme with the continuous multiwavelength pump scheme, it is found that the gain of the TDM pump scheme is higher than that of the continuous multiwavelength pump scheme.